add script_dump column from xcos_on_cloud

1 files changed, 24284 insertions, 311 deletions

diff --git a/blocks/saveAPI/fixtures/saveAPI.yaml b/blocks/saveAPI/fixtures/saveAPI.yaml
index 3a0e7e64..cacb8790 100644
--- a/blocks/saveAPI/fixtures/saveAPI.yaml
+++ b/blocks/saveAPI/fixtures/saveAPI.yaml
@@ -69,13 +69,13 @@
   fields:
     category_name: Power Systems
 - model: saveAPI.gallery
-  pk: 622
+  pk: 1
   fields:
     save_id: gallery0
     name: ch5_1
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 5) Analysis
       Methods, 5.1) The branch current method'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="ch51.scos"><!--Xcos - 1.0 - scilab-5.5.2
@@ -1054,14 +1054,15 @@
       x="300.0" y="190.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-5c1d823d:130d68ab7d2:-7f7c" parent="-5c1d823d:130d68ab7d2:-7f7b"/></XcosDiagram>
     media: gallery0.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 623
+  pk: 2
   fields:
     save_id: gallery1
     name: ch5_6
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 5) Analysis
       Methods, 5.6) Network reduction'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ch5_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -2727,14 +2728,15 @@
       scilabClass="ScilabList"><mxPoint x="630.0" y="450.0"/><mxPoint x="630.0" y="410.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="331568f2:130d6f18fe2:-8000" parent="331568f2:130d6f18fe2:-7fff"/></XcosDiagram>
     media: gallery1.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 624
+  pk: 3
   fields:
     save_id: gallery2
     name: ch5_7
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 5) Analysis
       Methods, 5.7) Superposition'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ch5_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -3634,14 +3636,15 @@
       x="844.0" y="90.0"/><mxPoint as="targetPoint" x="880.0" y="90.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="331568f2:130d6f18fe2:-7db5" parent="331568f2:130d6f18fe2:-7db4"/></XcosDiagram>
     media: gallery2.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 625
+  pk: 4
   fields:
     save_id: gallery3
     name: ch6_11
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 6) Amplifiers
       and Operational Amplifiers, 6.11) Noninverting circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="ch611"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -4342,14 +4345,15 @@
       x="640.0" y="200.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-55de3cf2:130fe0d1e6e:-7e33" parent="-55de3cf2:130fe0d1e6e:-7e32"/></XcosDiagram>
     media: gallery3.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 626
+  pk: 5
   fields:
     save_id: gallery4
     name: ch6_15
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 6) Amplifiers
       and Operational Amplifiers, 6.15) Circuits containing several Op amps'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ch6_15"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -5502,14 +5506,15 @@
       x="584.0" y="180.0"/><mxPoint as="targetPoint" x="610.0" y="180.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-1e985524:130d9355380:-8000" parent="-1e985524:130d9355380:-7fff"/></XcosDiagram>
     media: gallery4.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 627
+  pk: 6
   fields:
     save_id: gallery5
     name: ch6_9
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 6) Amplifiers
       and Operational Amplifiers, 6.9) Analysis of circuits containing ideal op amps'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ch6_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -7439,14 +7444,15 @@
       scilabClass="ScilabList"><mxPoint x="740.0" y="170.0"/><mxPoint x="740.0" y="130.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="5678f95b:130d8f27016:-8000" parent="5678f95b:130d8f27016:-7fff"/></XcosDiagram>
     media: gallery5.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 628
+  pk: 7
   fields:
     save_id: gallery6
     name: ch8_2
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.2) Capacitor Discharge in a Resistor'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.05" title="ch8_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -7976,14 +7982,15 @@
       scilabClass="ScilabList"><mxPoint x="120.0" y="110.0"/></Array></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-1e985524:130d9355380:-7dc3" parent="-1e985524:130d9355380:-7dc2"/></XcosDiagram>
     media: gallery6.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 629
+  pk: 8
   fields:
     save_id: gallery7
     name: ch8_3
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.3) Establishing a DC Voltage across a Capacitor'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.1" title="ch8_3"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -8549,14 +8556,15 @@
       x="430.0" y="84.0"/><mxPoint as="targetPoint" x="430.0" y="150.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-1e985524:130d9355380:-7d28" parent="-1e985524:130d9355380:-7d27"/></XcosDiagram>
     media: gallery7.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 630
+  pk: 9
   fields:
     save_id: gallery8
     name: ch8_4
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.4) The Source free RL Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.1" title="ch8_4"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -9606,14 +9614,15 @@
       x="-8.0" y="6.0"/></ExplicitInputPort></root></mxGraphModel><mxCell as="defaultParent"
       id="-1e985524:130d9355380:-7b0d" parent="-1e985524:130d9355380:-7b0c"/></XcosDiagram>
     media: gallery8.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 631
+  pk: 10
   fields:
     save_id: gallery9
     name: ch8_5
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.5) Complex first order RL and RC Circuits'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="ch8_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -10534,14 +10543,15 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="40.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-5c3e5c92:130db8fddce:-8000" parent="-5c3e5c92:130db8fddce:-7fff"/></XcosDiagram>
     media: gallery9.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 632
+  pk: 11
   fields:
     save_id: gallery10
     name: ch8_6
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.6) Complex first order RL and RC Circuits'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1.0" title="ch8_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -12375,14 +12385,15 @@
       x="210.0" y="190.0"/><mxPoint x="210.0" y="190.0"/><mxPoint x="160.0" y="190.0"/></Array></mxGeometry></ImplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="31befcfe:130dc407023:-8000" parent="31befcfe:130dc407023:-7fff"/></XcosDiagram>
     media: gallery10.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 633
+  pk: 12
   fields:
     save_id: gallery11
     name: ch8_7
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.7) DC Steady state in Inductors and Capacitors'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="ch8_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -13548,14 +13559,15 @@
       as="defaultParent" id="31befcfe:130dc407023:-7d8a" parent="31befcfe:130dc407023:-7d89"/><mxPoint
       as="origin" x="-6.0" y="-6.0"/></XcosDiagram>
     media: gallery11.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 634
+  pk: 13
   fields:
     save_id: gallery12
     name: ch8_8
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.8) DC Steady state in Inductors and Capacitors'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       title="ch8_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406 2040--><mxGraphModel
@@ -14320,14 +14332,15 @@
       as="targetPoint" x="360.0" y="360.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="4cf3be04:130e07e353b:-8000" parent="4cf3be04:130e07e353b:-7fff"/></XcosDiagram>
     media: gallery12.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 635
+  pk: 14
   fields:
     save_id: gallery13
     name: ch8_9
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 8) First
       order Circuits, 8.9) Transitions at Switching Time'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="ch8_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -15602,14 +15615,15 @@
       x="400.0" y="370.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery13.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 636
+  pk: 15
   fields:
     save_id: gallery14
     name: ch9_1
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 9) Higher
       order circuits and Complex frequency, 9.1) Series RLC Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       cellsLocked="1" finalIntegrationTime="0.05" title="ch9_1"><!--Xcos - 1.0 - scilab-5.5.2
@@ -16106,14 +16120,15 @@
       x="400.0" y="290.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="5f267dc3:130e0981282:-8000" parent="5f267dc3:130e0981282:-7fff"/></XcosDiagram>
     media: gallery14.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 637
+  pk: 16
   fields:
     save_id: gallery15
     name: ch9_2
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 9) Higher
       order circuits and Complex frequency, 9.2) Series RLC Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.05" title="ch9_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -16612,14 +16627,15 @@
       as="geometry" height="8.0" width="8.0" x="40.0" y="16.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="5f267dc3:130e0981282:-7ebc" parent="5f267dc3:130e0981282:-7ebb"/></XcosDiagram>
     media: gallery15.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 638
+  pk: 17
   fields:
     save_id: gallery16
     name: ch9_5
     description: 'Electric Circuits (Author: M. Navhi And J. A. Edminister), 9) Higher
       order circuits and Complex frequency, 9.5) Parallel RLC circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 154
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1.0" title="ch9_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -17181,14 +17197,15 @@
       x="380.0" y="240.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="5f267dc3:130e0981282:-7d6d" parent="5f267dc3:130e0981282:-7d6c"/></XcosDiagram>
     media: gallery16.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 639
+  pk: 18
   fields:
     save_id: gallery17
     name: example3_27
     description: 'Basic Electronics (Author: D. De), 3) Diode Circuits, 3.27) Find
       currents and voltages'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 181
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_27"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -17910,14 +17927,53 @@
       y="20.0"/><mxPoint x="240.0" y="20.0"/></Array></mxGeometry></ImplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-3721ad33:1314dc6b131:-8000" parent="-3721ad33:1314dc6b131:-7fff"/></XcosDiagram>
     media: gallery17.png
+    script_dump: '// Find currents and voltages
+
+      // Basic Electronics
+
+      // By Debashis De
+
+      // First Edition, 2010
+
+      // Dorling Kindersley Pvt. Ltd. India
+
+      // Example 3-27 in page 179
+
+
+      // Given data
+
+      //Diode acts as short circuited.Both diodes are forward biased
+
+      V1=0; // Voltage at junction 1 in V
+
+      V2=0; // Voltage at junction 2 in V
+
+
+      //Calculation
+
+      I1=(20-V1)/(20*10^3);
+
+      I2=(V2-(-10))/(20*10^3);
+
+
+      printf("I1 = %0.0e A\n",I1);
+
+      printf("I2 = %0.1e A",I2);
+
+
+      // Result
+
+      // I1 = 1 mA
+
+      // I2 = 0.5 mA'
 - model: saveAPI.gallery
-  pk: 640
+  pk: 19
   fields:
     save_id: gallery18
     name: example3_28
     description: 'Basic Electronics (Author: D. De), 3) Diode Circuits, 3.28) Find
       voltage across diode'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 181
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       title="example3_28"><!--Xcos - 1.0 - scilab-5.5.2 - 20200302--><mxGraphModel
@@ -18473,14 +18529,44 @@
       y="470.0"/><mxPoint x="510.0" y="200.0"/></Array></mxGeometry></ImplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-3721ad33:1314dc6b131:-7f87" parent="-3721ad33:1314dc6b131:-7f86"/></XcosDiagram>
     media: gallery18.png
+    script_dump: '// Find voltage across diode
+
+      // Basic Electronics
+
+      // By Debashis De
+
+      // First Edition, 2010
+
+      // Dorling Kindersley Pvt. Ltd. India
+
+      // Example 3-28 in page 180
+
+
+      // Given data
+
+      I=0.1075; // Cirremt across diode in A
+
+      Rd=1; // Internal resistance of diode in ohm
+
+
+      // Calculation
+
+      Vd=I*Rd;
+
+      printf("Voltage across diode = %0.4f V",Vd);
+
+
+      // Result
+
+      // Voltage across diode = 0.1075 V'
 - model: saveAPI.gallery
-  pk: 641
+  pk: 20
   fields:
     save_id: gallery19
     name: example3_30
     description: 'Basic Electronics (Author: D. De), 3) Diode Circuits, 3.30) Calculate
       R Il max'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:07+00:00
     book: 181
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_30"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -19120,14 +19206,52 @@
       x="780.0" y="130.0"/><mxPoint as="targetPoint" x="780.0" y="180.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-3721ad33:1314dc6b131:-7f5d" parent="-3721ad33:1314dc6b131:-7f5c"/></XcosDiagram>
     media: gallery19.png
+    script_dump: '// Calculate R,I_l(max)
+
+      // Basic Electronics
+
+      // By Debashis De
+
+      // First Edition, 2010
+
+      // Dorling Kindersley Pvt. Ltd. India
+
+      // Example 3-30 in page 181
+
+
+      // Given data
+
+      V_0=50; // Zener diode voltage in V
+
+      I_L=0; // Load current in A
+
+
+      // Calculation
+
+      R=(150)/(40*10^-3);
+
+      printf("(a)R = %0.2e ohm\n",R);
+
+      printf("I_L = I_max when Id = Id_min = 10mA\n");
+
+      I_Lmax=40-10;
+
+      printf("(b)Maximum load current = %0.0f mA",I_Lmax);
+
+
+      // Result
+
+      // (a) R = 3.75 K-ohms
+
+      // (b) I_Lmax = 30 mA'
 - model: saveAPI.gallery
-  pk: 642
+  pk: 21
   fields:
     save_id: gallery20
     name: example3_8
     description: 'Basic Electronics (Author: D. De), 3) Diode Circuits, 3.8) Calculate
       the dc load current'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 181
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       title="Ex3_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331 1216--><mxGraphModel
@@ -19793,14 +19917,71 @@
       x="870.0" y="200.0"/><mxPoint x="740.0" y="200.0"/></Array></mxGeometry></ImplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2d85d470:1314777ee15:-7f7e" parent="-2d85d470:1314777ee15:-7f7d"/></XcosDiagram>
     media: gallery20.png
+    script_dump: '// Calculate the dc load current
+
+      // Basic Electronics
+
+      // By Debashis De
+
+      // First Edition, 2010
+
+      // Dorling Kindersley Pvt. Ltd. India
+
+      // Example 3-8 in page 157
+
+
+      // Given data
+
+      Vm=280; // Supply voltage in V
+
+      Rl=2000; // Load resistance in ohms
+
+      Rf=500; // Internal resistance of the diodes in ohms
+
+
+      // Calculation
+
+      Idc=(2*Vm)/(%pi*2500);
+
+      Idc_t=Idc/2;
+
+      printf("(a)I_dc = %0.2e A\n(b)I_dc(tube) = %0.2e A\n",Idc,Idc_t);
+
+      printf("(c)Voltage across conducting diode is sinusoidal with a peak value 0.2
+      Vm\n");
+
+      V_rms=0.905*(280*sqrt(2));
+
+      Pdc=Idc^2*Rl;
+
+      R=(Rf/Rl)*100;
+
+      printf("Rms voltage V_rms = %0.0f V\n",V_rms);
+
+      printf("(d)DC output power = %0.1f W\n",Pdc);
+
+      printf("(e)Percentage regulation = %0.0f percent",R);
+
+
+      // Result
+
+      // (a) Idc = 71 mA,
+
+      // (b) Idc_tube = 35.7 mA,
+
+      // (c) V_rms = 358 V,
+
+      // (d) P_dc = 10.167W,
+
+      // (e) Percentage regulation = 25%'
 - model: saveAPI.gallery
-  pk: 643
+  pk: 22
   fields:
     save_id: gallery21
     name: Ex10_1
     description: 'Digital Control (Author: K. M. Moudgalya), 10) Special Cases of
       Pole Placement Control, 10.1) Effect of delay in control performance'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="stb_disc"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -22203,14 +22384,1082 @@
       as="geometry" height="40.0" width="40.0" x="40.0" y="320.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-7476484f:145f8cd2a3c:-7be9" parent="-7476484f:145f8cd2a3c:-7be8"/></XcosDiagram>
     media: gallery21.png
+    script_dump: '// Effect of delay in control performance
+
+      // 10.1
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      Ts = 1; B = 0.63; A = [1 -0.37];
+
+      k = 5;
+
+      if k<=0, k = 1; end
+
+      [zk,dzk] = zpowk(k);
+
+
+      // Desired transfer function
+
+      phi = [1 -0.5];
+
+      delta = 1; // internal model of step introduced
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,delta);
+
+
+      // simulation parameters for stb_disc.xcos
+
+      // y1: 0 to 1; u1: 0 to 1.2
+
+      st = 1.0; // desired change in setpoint
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+
+      // simulation parameters for stb_disc.xcos
+
+      N_var = 0; C = 0; D = 1; N = 1;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 644
+  pk: 23
   fields:
     save_id: gallery22
     name: Ex10_2
     description: 'Digital Control (Author: K. M. Moudgalya), 10) Special Cases of
       Pole Placement Control, 10.2) Smith predictor for paper machine control'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="smith_disc"><!--Xcos - 1.0 - scilab-5.5.2
@@ -24769,14 +26018,1114 @@
       as="geometry" height="30.0" width="40.0" x="550.0" y="380.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-5d8a58f8:147c67c0236:-7ffb" parent="-5d8a58f8:147c67c0236:-7ffa"/></XcosDiagram>
     media: gallery22.png
+    script_dump: '// Smith predictor for paper machine control in Example 10.2 on
+      page 385.
+
+      // 10.2
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      function [C,degC] = poladd(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= cB | rA ~= rB
+
+      error(''poladd: Inconsistent dimensions'');
+
+      end
+
+
+      degC = max(degA,degB);
+
+      if degC >= degA
+
+      A = [A zeros(rA,(degC-degA)*cA)];
+
+      end
+
+      if degC >= degB
+
+      B = [B zeros(rB,(degC-degB)*cB)];
+
+      end
+
+      C = A+B;
+
+      endfunction;
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      Ts = 1; B = 0.63; A = [1 -0.37]; k = 3;
+
+      Bd = convol(B,[0 1]);
+
+      kd = k - 1;
+
+      [zkd,dzkd] = zpowk(kd);
+
+      [mzkd,dmzkd] = poladd(1,0,-zkd,dzkd);
+
+
+      // Desired transfer function
+
+      phi = [1 -0.5]; delta = 1;
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,1,phi,delta);
+
+
+      // simulation parameters for smith_disc.xcos
+
+      st = 1.0; // desired change in setpoint
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+
+      // simulation parameters for smith_disc.xcos
+
+      N_var = 0; C = 0; D = 1; N = 1;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bdp,Ap] = cosfil_ip(Bd,A); // Bd/Ad
+
+      [zkdp1,zkdp2] = cosfil_ip(zkd,1); // zkd/1
+
+      [mzkdp1,mzkdp2] = cosfil_ip(mzkd,1); // mzkd/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 645
+  pk: 24
   fields:
     save_id: gallery23
     name: Ex11_4
     description: 'Digital Control (Author: K. M. Moudgalya), 11) Minimum Variance
       Control, 11.4) 1st control problem by MacGregor'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1000.0" title="stb_disc"><!--Xcos - 1.0 - scilab-5.5.2
@@ -27179,14 +29528,1299 @@
       as="geometry" height="40.0" width="40.0" x="40.0" y="320.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-7476484f:145f8cd2a3c:-7be9" parent="-7476484f:145f8cd2a3c:-7be8"/></XcosDiagram>
     media: gallery23.png
+    script_dump: '// MacGregor''s first control problem, discussed in Example 11.4
+      on page 213.
+
+      // 11.4
+
+      // Minimum variance control law design, given by Eq. 11.40 on page 413.
+
+      // 11.5
+
+
+      // function [S,dS,R,dR] = mv(A,dA,B,dB,C,dC,k,int)
+
+      // implements the minimum variance controller
+
+      // if int>=1, integrated noise is assumed; otherwise,
+
+      // it is not integrated noise
+
+
+      function [S,dS,R,dR] = mv(A,dA,B,dB,C,dC,k,int1)
+
+      zk = zeros(1,k+1); zk(k+1) = 1;
+
+      if int1>=1, [A,dA] = polmul([1 -1],1,A,dA); end
+
+      [Fk,dFk,Ek,dEk] = xdync(zk,k,A,dA,C,dC);
+
+
+      [Gk,dGk] = polmul(Ek,dEk,B,dB);
+
+      S = Fk; dS = dFk; R = Gk; dR = dGk;
+
+      endfunction;
+
+      // Calculation of closed loop transfer functions
+
+      // 11.6
+
+
+      // function [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+
+      //    cl(A,dA,B,dB,C,dC,k,S,dS,R,dR,int)
+
+      // int>=1 means integrated noise and control law:
+
+      // delta u = - (S/R)y
+
+      // Evaluates the closed loop transfer function and
+
+      // variances of input and output
+
+
+      function [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+
+      cl(A,dA,B,dB,C,dC,k,S,dS,R,dR,int1)
+
+      [zk,dzk] = zpowk(k);
+
+
+      [BS,dBS] = polmul(B,dB,S,dS);
+
+      [zBS,dzBS] = polmul(zk,dzk,BS,dBS);
+
+      [RA,dRA] = polmul(R,dR,A,dA);
+
+      if int1>=1, [RA,dRA] = polmul(RA,dRA,[1 -1],1); end
+
+
+      [D,dD] = poladd(RA,dRA,zBS,dzBS);
+
+
+      [Ny,dNy] = polmul(C,dC,R,dR);
+
+      [Nu,dNu] = polmul(C,dC,S,dS);
+
+
+      [Nu,dNu,Du,dDu,uvar] = tfvar(Nu,dNu,D,dD);
+
+      [Ny,dNy,Dy,dDy,yvar] = tfvar(Ny,dNy,D,dD);
+
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      function [C,degC] = poladd(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= cB | rA ~= rB
+
+      error(''poladd: Inconsistent dimensions'');
+
+      end
+
+
+      degC = max(degA,degB);
+
+      if degC >= degA
+
+      A = [A zeros(rA,(degC-degA)*cA)];
+
+      end
+
+      if degC >= degB
+
+      B = [B zeros(rB,(degC-degB)*cB)];
+
+      end
+
+      C = A+B;
+
+      endfunction;
+
+      // Cancellation of common factors and determination of covariance
+
+      // 11.7
+
+
+      // function [N,dN,D,dD,yvar] = tfvar(N,dN,D,dD)
+
+      // N and D polynomials in z^{-1} form; discrete case
+
+
+      function [N,dN,D,dD,yvar] = tfvar(N,dN,D,dD)
+
+
+      [N,dN,D,dD] = l2r(N,dN,D,dD);
+
+      N = N/D(1); D = D/D(1);
+
+      LN = length(N); LD = length(D);
+
+      D1 = D;
+
+      if LD<LN, D1 = [D zeros(1,LN-LD)]; dD1 = dD+LN-LD; end
+
+      H = tf(N,D1,1);//TS=1 (sampling time) has been taken constant in tfvar
+
+      yvar = covar_m(H,1);
+
+      endfunction;
+
+      // function [Rnum,Rnumdeg,Rden,Rdendeg] = l2r(N,degN,D,degD)
+
+      // given Numerator and Denominator polynomial matrices in left form,
+
+      // not necessarily coprime, finds right coprime factorisation.
+
+
+      function [Rnum,Rnumdeg,Rden,Rdendeg] = l2r(N,degN,D,degD)
+
+
+      [N,degN] = transp(N,degN);
+
+      [D,degD] = transp(D,degD);
+
+
+      [Rnum,Rnumdeg,Rden,Rdendeg] = left_prm(N,degN,D,degD);
+
+      [Rnum,Rnumdeg] = transp(Rnum,Rnumdeg);
+
+      [Rden,Rdendeg] = transp(Rden,Rdendeg);
+
+      endfunction;
+
+      // function [P,degP] = transp(Q,degQ)
+
+      // MATLAB FUNCTION transp TO TRANSPOSE
+
+      // A POLYNOMIAL MATRIX
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = transp(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      rP = cQ; cP = rQ; degP = degQ;
+
+      P = zeros(rP,(degP+1)*cP);
+
+      for i = 1:degP+1
+
+      P(:,(i-1)*cP+1:i*cP) = Q(:,(i-1)*cQ+1:i*cQ)'';
+
+      end
+
+
+      endfunction;
+
+      //User defined function
+
+      //Forms a transfer function
+
+      //Scilab: Co efficients are given in increasing power of variable
+
+      //Matlab: Co efficients are given in decreasing power of variable
+
+      //Hence co efficients are flipped here
+
+
+      //Input arguments: (1) Numerator co efficients(decreasing order)
+
+      //(2) Denominator co efficients
+
+      //(3) Variable to specify domain
+
+
+      // Updated (30-11-06)
+
+      // System is continuous => a is not passed
+
+      // System is discrete => a = -1
+
+      // System is discretized (sampled system) => a = Ts
+
+      // Uses syslin
+
+
+      function trfu = tf(num,den,a)
+
+      if argn(2) == 2
+
+      d = ''c'';
+
+      elseif a == -1
+
+      d = ''d'';
+
+      else
+
+      d = a
+
+      end;
+
+      num = clean(num);
+
+      den = clean(den);
+
+      num1 = poly(num(length(num):-1:1),''x'',''coeff'');
+
+      den1 = poly(den(length(den):-1:1),''x'',''coeff'');
+
+      trfu = syslin(d,num1,den1);
+
+      endfunction;
+
+
+
+
+      //User defined equivalent function to Matlab covar function
+
+      //For discrete time domain only
+
+      //Uses Lyapunov''s equation for computation
+
+      //W: noise intensity (scalar)
+
+      //Matlab result for unstable systems:
+
+      //Warning: Unstable models have infinite covariance
+
+
+      function P = covar_m(sys,W)
+
+      a = roots(sys(''den''));
+
+      b = length(a);
+
+      c = abs(a) > 1;
+
+      if b ~= 0 then
+
+      for i = 1:b
+
+      if c(i) == %t then
+
+      disp(''Warning: System being unstable has infinite covariance'');
+
+      P = %inf;
+
+      else
+
+      s = tf2ss(sys);
+
+      [A,B,C,D] = s(2:5);
+
+      //Sylvester and Lyapunov solver
+
+      task = 2; flag = [1 0]; tran = 1;
+
+      Q1 = -B*W*B'';
+
+      Q = linmeq(task,A,Q1,flag,tran)
+
+      P = C*Q*C'' + D*W*D'';
+
+      end;
+
+      end;
+
+      else
+
+      s = tf2ss(sys);
+
+      [A,B,C,D] = s(2:5);
+
+      //Sylvester and Lyapunov solver
+
+      task = 2; flag = [1 0]; tran = 1;
+
+      Q1 = -B*W*B'';
+
+      Q = linmeq(task,A,Q1,flag,tran)
+
+      P = C*Q*C'' + D*W*D'';
+
+      end;
+
+      endfunction;
+
+
+      //if d==0 | c==%f
+
+      //  disp(''Calc'');
+
+      //else
+
+      //  disp(''Unstable'');
+
+      //end;
+
+      // Above logic can also solve our purpose
+
+      // But it gives incorrect answer if roots are [1 -1 1] or
+
+      // [1 -1 -1] ....
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // MacGregor''s first control problem
+
+      A = [1 -1.4 0.45]; dA = 2; C = [1 -0.5]; dC = 1;
+
+      B = 0.5*[1 -0.9]; dB = 1; k = 1; int1 = 0;
+
+      [Sc,dSc,Rc,dRc] = mv(A,dA,B,dB,C,dC,k,int1);
+
+      [Nu,dNu,Du,dDu,Ny,dNy,Dy,dDy,yvar,uvar] = ...
+
+      cl(A,dA,B,dB,C,dC,k,Sc,dSc,Rc,dRc,int1);
+
+
+      // Simulation parameters for stb_disc.xcos
+
+      Tc = Sc; gamm = 1; [zk,dzk] = zpowk(k);
+
+      D = 1; N_var = 1; Ts = 1; st = 0;
+
+      t_init = 0; t_final = 1000;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 646
+  pk: 25
   fields:
     save_id: gallery24
     name: Ex7_6
     description: 'Digital Control (Author: K. M. Moudgalya), 7) Structures and Specifications,
       7.6) Verification of performance of lead controller on antenna system'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="g_s_cl2"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -29734,14 +33368,142 @@
       as="geometry" height="40.0" width="40.0" x="460.0" y="360.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-75a601dc:14604d880d0:-7ffd" parent="-75a601dc:14604d880d0:-7ffc"/></XcosDiagram>
     media: gallery24.png
+    script_dump: '// Verification of performance of lead controller on antenna system,
+      as discussed in Example 7.3.
+
+      // 7.6
+
+
+      // Continuous time antenna model
+
+      a = 0.1;
+
+      F = [0 1;0 -a]; g = [0; a]; c = [1 0]; d = 0;
+
+      Ga = syslin(''c'',F,g,c,d); [ds,num,den] = ss2tf(Ga);
+
+      Num = clean(num); Den = clean(den);
+
+      Ts = 0.2;
+
+      G = dscr(Ga,Ts);
+
+
+      // lead controller
+
+      beta1 = 0.8;
+
+      N = [1 -0.9802]*(1-beta1)/(1-0.9802); Rc = [1 -beta1];
+
+
+      // simulation parameters using g_s_cl2.cos
+
+      gamm = 1; Sc = 1; Tc = 1; C = 0; D = 1;
+
+      st = 1; st1 = 0;
+
+      t_init = 0; t_final = 20;
+
+
+      // u1: -4 to 11
+
+      // y1: 0 to 1.4
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 647
+  pk: 26
   fields:
     save_id: gallery25
     name: Ex7_7
     description: 'Digital Control (Author: K. M. Moudgalya), 7) Structures and Specifications,
       7.7) Illustration of system type'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="stb_disc"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -32157,14 +35919,1008 @@
       as="geometry" height="40.0" width="40.0" x="40.0" y="320.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-7476484f:145f8cd2a3c:-7be9" parent="-7476484f:145f8cd2a3c:-7be8"/></XcosDiagram>
     media: gallery25.png
+    script_dump: '// Illustration of system type, as explained in Example 7.10 on
+      page 275.
+
+      // 7.7
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // Solution to Aryabhatta''s identity arising in PID controller design, namely
+      Eq. 9.37 on page 363.
+
+      // 9.20
+
+
+      function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      dB = length(B) - 1; dA = length(A) - 1;
+
+      [zk,dzk] = zpowk(k);
+
+      [N,dN] = polmul(B,dB,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(A,dA,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+      [Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+
+      Rc = convol(R,Delta);
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Plant
+
+      B = 1; A = [1 -1]; zk = [0 1]; Ts = 1; k = 1;
+
+      // Value of k absent in original code
+
+      // Specify closed loop characteristic polynomial
+
+      phi = [1 -0.5];
+
+
+      // Design the controller
+
+      reject_ramps = 1;
+
+      if reject_ramps == 1,
+
+      Delta = [1 -1]; // to reject ramps another Delta
+
+      else
+
+      Delta = 1; // steps can be rejected by plant itself
+
+      end
+
+      [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+
+      // parameters for simulation using stb_disc.mdl
+
+      Tc = Sc; gamm = 1; N = 1;
+
+      C = 0; D = 1; N_var = 0;
+
+      st = 1; t_init = 0; t_final = 20;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+      // Give appropriate path
+
+      //xcos(''stb_disc.xcos'');'
 - model: saveAPI.gallery
-  pk: 648
+  pk: 27
   fields:
     save_id: gallery26
     name: Ex9_10
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.10) Pole placement controller IBM Lotus Domino server'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="40.0" title="Ex9_10"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -34512,14 +39268,1101 @@
       as="defaultParent" id="-2f864670:16fc63faf34:-7bc7" parent="-2f864670:16fc63faf34:-7bc6"/><mxPoint
       as="origin" x="-80.0"/></XcosDiagram>
     media: gallery26.png
+    script_dump: '// Pole placement controller IBM Lotus Domino server, discussed
+      in Example 9.9 on page 341.
+
+      // 9.10
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Control of IBM lotus domino server
+
+      // Transfer function
+
+      B = 0.47; A = [1 -0.43]; k = 1;
+
+      [zk,dzk] = zpowk(k);
+
+
+      // Transient specifications
+
+      rise = 10; epsilon = 0.01; Ts = 1;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = [1 -1];  // internal model of step used
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+
+      // Simulation parameters for stb_disc.xcos
+
+      st = 1; // desired change
+
+      t_init = 0; // simulation start time
+
+      t_final = 40; // simulation end time
+
+      C = 0; D = 1; N_var = 0;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 649
+  pk: 28
   fields:
     save_id: gallery27
     name: Ex9_11
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.11) Pole placement controller for motor problem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="Untitled - 10:43:53 AM"><!--Xcos - 1.0 -
@@ -36812,14 +42655,1141 @@
       as="points" scilabClass=""><mxPoint x="520.0" y="450.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2f864670:16fc63faf34:-759a" parent="-2f864670:16fc63faf34:-7599"/></XcosDiagram>
     media: gallery27.png
+    script_dump: '// Pole placement controller for motor problem, discussed in Example
+      9.10 on page 343.
+
+      // 9.11
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Motor control problem
+
+      // Transfer function
+
+      a1 = [-1 0; 1 0]; b1 = [1; 0]; c1 = [0 1]; d1 = 0;
+
+      G = syslin(''c'',a1,b1,c1,d1); Ts = 0.25;
+
+      [B,A,k] = myc2d(G,Ts);
+
+
+      // Transient specifications
+
+      rise = 3; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = 1; // No internal model of step used
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+
+      // simulation parameters for c_ss_cl.xcos
+
+      st = 1;  //desired change in position
+
+      t_init = 0;  //simulation start time
+
+      t_final = 10;  //simulation end time
+
+      xInitial = [0 0];  //initial conditions
+
+      N = 1; C = 0; D = 1; N_var = 0;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 650
+  pk: 29
   fields:
     save_id: gallery28
     name: Ex9_14
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.14) Controller design'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1.5" title="Ex9_14"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -39360,14 +46330,1251 @@
       as="geometry" height="40.0" width="40.0" x="680.0" y="400.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-2f864670:16fc63faf34:-72c4" parent="-2f864670:16fc63faf34:-72c3"/></XcosDiagram>
     media: gallery28.png
+    script_dump: '// Controller design for the case study presented in Example 9.12
+      on page 347.
+
+      // 9.14
+
+
+      //User defined function
+
+      //Forms a transfer function
+
+      //Scilab: Co efficients are given in increasing power of variable
+
+      //Matlab: Co efficients are given in decreasing power of variable
+
+      //Hence co efficients are flipped here
+
+
+      //Input arguments: (1) Numerator co efficients(decreasing order)
+
+      //(2) Denominator co efficients
+
+      //(3) Variable to specify domain
+
+
+      // Updated (30-11-06)
+
+      // System is continuous => a is not passed
+
+      // System is discrete => a = -1
+
+      // System is discretized (sampled system) => a = Ts
+
+      // Uses syslin
+
+
+      function trfu = tf(num,den,a)
+
+      if argn(2) == 2
+
+      d = ''c'';
+
+      elseif a == -1
+
+      d = ''d'';
+
+      else
+
+      d = a
+
+      end;
+
+      num = clean(num);
+
+      den = clean(den);
+
+      num1 = poly(num(length(num):-1:1),''x'',''coeff'');
+
+      den1 = poly(den(length(den):-1:1),''x'',''coeff'');
+
+      trfu = syslin(d,num1,den1);
+
+      endfunction;
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1;
+
+      end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // Pole placement controller without intra sample oscillations, as discussed
+      in Sec. 9.5.
+
+      // 9.13
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im2(B,A,k,phi,Delta,a)
+
+      // 2-DOF PP controller with internal model of Delta and without
+
+      // hidden oscillations
+
+
+      function [Rc,Sc,Tc,gamm,phit] = pp_im2(B,A,k,phi,Delta,a)
+
+
+      if argn(2) == 5, a = 1; end
+
+      dphi = length(phi)-1;
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A,a); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B,a); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      // Total characteristic polynomial
+
+      phit = convol(phi,convol(Ag,Bg));
+
+      endfunction;
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      num = 200;
+
+      den = convol([0.05 1],[0.05 1]);
+
+      den = convol([10 1],den);
+
+      G = tf(num,den); Ts = 0.025;
+
+      num = G(''num''); den = G(''den'');
+
+      // iodel = 0;
+
+      [B,A,k] = myc2d(G,Ts);
+
+      [zk,dzk] = zpowk(k); //int1 = 0;
+
+
+      // Transient specifications
+
+      a = 0.9; rise = 0.24; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = [1 -1]; // internal model of step is present
+
+      [Rc,Sc,Tc,gamm] = pp_im2(B,A,k,phi,Delta,a);
+
+
+      // margin calculation
+
+      Lnum = convol(Sc,convol(B,zk));
+
+      Lden = convol(Rc,A);
+
+      L = tf(Lnum,Lden,Ts);
+
+      // Gm = g_margin(L); //---- Does not match --------------- (in dB)
+
+      Pm = p_margin(L); //---- Convergence problem --------------- (in degree)
+
+
+      num1 = 100; den1 = [10 1];
+
+      Gd = tf(num1,den1);  //-------
+
+      [C,D,k1] = myc2d(Gd,Ts);
+
+      [zk,dzk] = zpowk(k);
+
+      C = convol(C,zk);
+
+
+      // simulation parameters g_s_cl2.xcos ------------
+
+      N = 1;
+
+      st = 1; // desired change in setpoint
+
+      st1 = 0; // magnitude of disturbance
+
+      t_init = 0; // simulation start time
+
+      t_final = 1.5; // simulation end time
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 651
+  pk: 30
   fields:
     save_id: gallery29
     name: Ex9_15_1
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.15) Evaluation of continuous time controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex9_15_1"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -41866,14 +50073,308 @@
       as="geometry" height="40.0" width="40.0" x="760.0" y="420.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-2f864670:16fc63faf34:-6b2d" parent="-2f864670:16fc63faf34:-6b2c"/></XcosDiagram>
     media: gallery29.png
+    script_dump: '// Evaluation of continuous time controller for the case study presented
+      in Example 9.13 on page 349.
+
+      // 9.15
+
+
+      //User defined function
+
+      //Forms a transfer function
+
+      //Scilab: Co efficients are given in increasing power of variable
+
+      //Matlab: Co efficients are given in decreasing power of variable
+
+      //Hence co efficients are flipped here
+
+
+      //Input arguments: (1) Numerator co efficients(decreasing order)
+
+      //(2) Denominator co efficients
+
+      //(3) Variable to specify domain
+
+
+      // Updated (30-11-06)
+
+      // System is continuous => a is not passed
+
+      // System is discrete => a = -1
+
+      // System is discretized (sampled system) => a = Ts
+
+      // Uses syslin
+
+
+      function trfu = tf(num,den,a)
+
+      if argn(2) == 2
+
+      d = ''c'';
+
+      elseif a == -1
+
+      d = ''d'';
+
+      else
+
+      d = a
+
+      end;
+
+      num = clean(num);
+
+      den = clean(den);
+
+      num1 = poly(num(length(num):-1:1),''x'',''coeff'');
+
+      den1 = poly(den(length(den):-1:1),''x'',''coeff'');
+
+      trfu = syslin(d,num1,den1);
+
+      endfunction;
+
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      num = 200;
+
+      den = convol([0.05 1],[0.05 1]);
+
+      den = convol([10 1],den);
+
+      G = tf(num,den); Ts = 0.005;
+
+      [B,A,k] = myc2d(G,Ts);
+
+      [zk,dzk] = zpowk(k); //int = 0;
+
+
+      // Sigurd''s feedback controller''
+
+      numb = 0.5*convol([1 2],[0.05 1]);
+
+      denb = convol([1 0],[0.005 1]);
+
+      Gb = tf(numb,denb);
+
+      [Sb,Rb,kb] = myc2d(Gb,Ts);
+
+      [zkb,dzkb] = zpowk(kb);
+
+      Sb = convol(Sb,zkb);
+
+
+      // Sigurd''s feed forward controller''
+
+      numf = [0.5 1];
+
+      denf = convol([0.65 1],[0.03 1]);
+
+      Gf = tf(numf,denf);
+
+      [Sf,Rf,kf] = myc2d(Gf,Ts);
+
+      [zkf,dzkf] = zpowk(kf);
+
+      Sf = convol(Sf,zkf);
+
+
+      // Margins
+
+      simp_mode(%f);
+
+      L = G*Gb;
+
+      // Gm = g_margin(L); // ------
+
+      Pm = p_margin(L); // ------
+
+      Lnum = convol(Sb,convol(zk,B));
+
+      Lden = convol(Rb,A);
+
+      L = tf(Lnum,Lden,Ts);
+
+      // DGm = g_margin(L); // ------
+
+      DPm = p_margin(L); // ------
+
+
+      // Noise
+
+      num1 = 100; den1 = [10 1];
+
+
+      // simulation parameters for
+
+      // entirely continuous simulation: g_s_cl3.xcos
+
+      // hybrid simulation: g_s_cl6.xcos
+
+      st = 1; // desired change in setpoint
+
+      st1 = 0;
+
+      t_init = 0; // simulation start time
+
+      t_final = 5; // simulation end time
+
+
+      num = polyno(num,''s''); den = polyno(den,''s'');
+
+      Numb = polyno(numb,''s''); Denb = polyno(denb,''s'');
+
+      Numf = polyno(numf,''s''); Denf = polyno(denf,''s'');
+
+      Num1 = polyno(num1,''s''); Den1 = polyno(den1,''s'');
+
+
+      [Sbp,Rbp] = cosfil_ip(Sb,Rb);
+
+      [Sfp,Rfp] = cosfil_ip(Sf,Rf);'
 - model: saveAPI.gallery
-  pk: 652
+  pk: 31
   fields:
     save_id: gallery30
     name: Ex9_15_2
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.15) Evaluation of continuous time controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex9_15_2"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -44481,14 +52982,308 @@
       as="defaultParent" id="-2f864670:16fc63faf34:-6546" parent="-2f864670:16fc63faf34:-6545"/><mxPoint
       as="origin" y="-10.0"/></XcosDiagram>
     media: gallery30.png
+    script_dump: '// Evaluation of continuous time controller for the case study presented
+      in Example 9.13 on page 349.
+
+      // 9.15
+
+
+      //User defined function
+
+      //Forms a transfer function
+
+      //Scilab: Co efficients are given in increasing power of variable
+
+      //Matlab: Co efficients are given in decreasing power of variable
+
+      //Hence co efficients are flipped here
+
+
+      //Input arguments: (1) Numerator co efficients(decreasing order)
+
+      //(2) Denominator co efficients
+
+      //(3) Variable to specify domain
+
+
+      // Updated (30-11-06)
+
+      // System is continuous => a is not passed
+
+      // System is discrete => a = -1
+
+      // System is discretized (sampled system) => a = Ts
+
+      // Uses syslin
+
+
+      function trfu = tf(num,den,a)
+
+      if argn(2) == 2
+
+      d = ''c'';
+
+      elseif a == -1
+
+      d = ''d'';
+
+      else
+
+      d = a
+
+      end;
+
+      num = clean(num);
+
+      den = clean(den);
+
+      num1 = poly(num(length(num):-1:1),''x'',''coeff'');
+
+      den1 = poly(den(length(den):-1:1),''x'',''coeff'');
+
+      trfu = syslin(d,num1,den1);
+
+      endfunction;
+
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      num = 200;
+
+      den = convol([0.05 1],[0.05 1]);
+
+      den = convol([10 1],den);
+
+      G = tf(num,den); Ts = 0.005;
+
+      [B,A,k] = myc2d(G,Ts);
+
+      [zk,dzk] = zpowk(k); //int = 0;
+
+
+      // Sigurd''s feedback controller''
+
+      numb = 0.5*convol([1 2],[0.05 1]);
+
+      denb = convol([1 0],[0.005 1]);
+
+      Gb = tf(numb,denb);
+
+      [Sb,Rb,kb] = myc2d(Gb,Ts);
+
+      [zkb,dzkb] = zpowk(kb);
+
+      Sb = convol(Sb,zkb);
+
+
+      // Sigurd''s feed forward controller''
+
+      numf = [0.5 1];
+
+      denf = convol([0.65 1],[0.03 1]);
+
+      Gf = tf(numf,denf);
+
+      [Sf,Rf,kf] = myc2d(Gf,Ts);
+
+      [zkf,dzkf] = zpowk(kf);
+
+      Sf = convol(Sf,zkf);
+
+
+      // Margins
+
+      simp_mode(%f);
+
+      L = G*Gb;
+
+      // Gm = g_margin(L); // ------
+
+      Pm = p_margin(L); // ------
+
+      Lnum = convol(Sb,convol(zk,B));
+
+      Lden = convol(Rb,A);
+
+      L = tf(Lnum,Lden,Ts);
+
+      // DGm = g_margin(L); // ------
+
+      DPm = p_margin(L); // ------
+
+
+      // Noise
+
+      num1 = 100; den1 = [10 1];
+
+
+      // simulation parameters for
+
+      // entirely continuous simulation: g_s_cl3.xcos
+
+      // hybrid simulation: g_s_cl6.xcos
+
+      st = 1; // desired change in setpoint
+
+      st1 = 0;
+
+      t_init = 0; // simulation start time
+
+      t_final = 5; // simulation end time
+
+
+      num = polyno(num,''s''); den = polyno(den,''s'');
+
+      Numb = polyno(numb,''s''); Denb = polyno(denb,''s'');
+
+      Numf = polyno(numf,''s''); Denf = polyno(denf,''s'');
+
+      Num1 = polyno(num1,''s''); Den1 = polyno(den1,''s'');
+
+
+      [Sbp,Rbp] = cosfil_ip(Sb,Rb);
+
+      [Sfp,Rfp] = cosfil_ip(Sf,Rf);'
 - model: saveAPI.gallery
-  pk: 653
+  pk: 32
   fields:
     save_id: gallery31
     name: Ex9_16
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.16) System type with 2 DOF controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="Ex9_16"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -46908,14 +55703,1068 @@
       as="defaultParent" id="-2f864670:16fc63faf34:-5f92" parent="-2f864670:16fc63faf34:-5f91"/><mxPoint
       as="origin" x="-350.0"/></XcosDiagram>
     media: gallery31.png
+    script_dump: '// System type with 2-DOF controller. It is used to arrive at the
+      results Example 9.14.
+
+      // 9.16
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      B = 1; A = [1 -1]; k = 1; zk = zpowk(k); Ts = 1;
+
+      phi = [1 -0.5];
+
+
+      Delta = 1; // Choice of internal model of step
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+
+      // simulation parameters for stb_disc.xcos
+
+      st = 1; // desired step change
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+      xInitial = [0 0];
+
+      C = 0; D = 1; N_var = 0;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 654
+  pk: 33
   fields:
     save_id: gallery32
     name: Ex9_17
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.17) Illustrating the benefit of cancellation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="Ex9_17"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -49329,14 +59178,1056 @@
       as="defaultParent" id="-2f864670:16fc63faf34:-5c8f" parent="-2f864670:16fc63faf34:-5c8e"/><mxPoint
       as="origin" x="-60.0"/></XcosDiagram>
     media: gallery32.png
+    script_dump: '// Illustrating the benefit of cancellation. It is used to arrive
+      at the results of Example 9.15.
+
+      // 9.17
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Solution to Aryabhatta''s identity arising in PID controller design, namely
+      Eq. 9.37 on page 363.
+
+      // 9.20
+
+
+      function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      dB = length(B) - 1; dA = length(A) - 1;
+
+      [zk,dzk] = zpowk(k);
+
+      [N,dN] = polmul(B,dB,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(A,dA,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+      [Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+
+      Rc = convol(R,Delta);
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // test problem to demonstrate benefits of 2_dof
+
+      // Ts = 1; B = [1 0.9]; A = conv([1 -1],[1 -0.8]); k = 1;
+
+      Ts = 1; k = 1;
+
+      B = convol([1 0.9],[1 -0.8]); A = convol([1 -1],[1 -0.5]);
+
+
+      // closed loop characteristic polynomial
+
+      phi = [1 -1 0.5];
+
+
+      Delta = 1; // Choice of internal model of step
+
+      control = 1;
+
+      if control == 1, // 1-DOF with no cancellation
+
+      [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+      Tc = Sc; gamm = 1;
+
+      else // 2-DOF
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+      end
+
+
+      // simulation parameters for stb_disc.mdl
+
+      [zk,dzk] = zpowk(k);
+
+      st = 1; // desired step change
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+      xInitial = [0 0];
+
+      C = 0; D = 1; N_var = 0;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 655
+  pk: 34
   fields:
     save_id: gallery33
     name: Ex9_18
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.18) Anti windup control of IBM Lotus Domino server'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1000.0" title="stb_disc_sat"><!--Xcos - 1.0 - scilab-5.5.2
@@ -52361,14 +63252,1223 @@
       as="geometry" height="20.0" width="60.0" x="670.0" y="160.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-98b0b2b:146d610f05a:-78c3" parent="-98b0b2b:146d610f05a:-78c2"/></XcosDiagram>
     media: gallery33.png
+    script_dump: '// Anti windup control (AWC) of IBM Lotus Domino server, studied
+      in Example 9.16 on page 357. It can be used for the follwoing situations: with
+      and without saturation, and with and without AWC.
+
+      // 9.18
+
+      // Pole placement controller without intra sample oscillations, as discussed
+      in Sec. 9.5.
+
+      // 9.13
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im2(B,A,k,phi,Delta,a)
+
+      // 2-DOF PP controller with internal model of Delta and without
+
+      // hidden oscillations
+
+
+      function [Rc,Sc,Tc,gamm,phit] = pp_im2(B,A,k,phi,Delta,a)
+
+
+      if argn(2) == 5, a = 1; end
+
+      dphi = length(phi)-1;
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A,a); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B,a); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      // Total characteristic polynomial
+
+      phit = convol(phi,convol(Ag,Bg));
+
+      endfunction;
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1;
+
+      end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+      function [C,degC] = poladd(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= cB | rA ~= rB
+
+      error(''poladd: Inconsistent dimensions'');
+
+      end
+
+
+      degC = max(degA,degB);
+
+      if degC >= degA
+
+      A = [A zeros(rA,(degC-degA)*cA)];
+
+      end
+
+      if degC >= degB
+
+      B = [B zeros(rB,(degC-degB)*cB)];
+
+      end
+
+      C = A+B;
+
+      endfunction;
+
+
+      //  Transfer function
+
+      B = 0.47; A = [1 -0.43]; k = 1;
+
+      [zk,dzk] = zpowk(k);
+
+
+      // Transient specifications
+
+      rise = 10; epsilon = 0.01; Ts = 1;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      delta = [1 -1]; // internal model of step used
+
+      [Rc,Sc,Tc,gamm,F] = pp_im2(B,A,k,phi,delta);
+
+
+      // Study of Antiwindup Controller
+
+
+      // Set key between 1 and 4
+
+      // key = 1: Simulate without any saturation limits
+
+      // key = 2: Simulate saturation, but do not use AWC
+
+      // key = 3: Simulate saturation with AWC in place
+
+      // key = 4: Simulate with AWC, without saturation limits
+
+      key=1
+
+
+      if key ==0
+
+      disp(''Invalid choice'');
+
+      return;
+
+      elseif key == 1
+
+      U = 2; L = -2; P = 1; F = Rc; E = 0; PSc = Sc; PTc = Tc;
+
+      elseif key == 2
+
+      U = 1; L = -1; P = 1; F = Rc; E = 0; PSc = Sc; PTc = Tc;
+
+      else
+
+      if key == 3 // Antiwindup controller and with saturation
+
+      U = 1; L = -1;
+
+      elseif key == 4 // Antiwindup controller, but no saturation
+
+      U = 2; L = -2;
+
+      else
+
+      disp(''Invalid choice'');
+
+      return;
+
+      end
+
+      P = A;
+
+      dF = length(F) - 1;
+
+      PRc = convol(P,Rc); dPRc = length(PRc) - 1;
+
+      [E,dE] = poladd(F,dF,-PRc,dPRc);
+
+      PSc = convol(P,Sc); PTc = convol(P,Tc);
+
+      end
+
+
+      // Setting up simulation parameters for stb_disc_sat
+
+      t_init = 0; // first step begins
+
+      st = 1; // height of first step
+
+      t_init2 = 500; // second step begins
+
+      st2 = -2; // height of second step
+
+      t_final = 1000; // simulation end time
+
+      st1 = 0; // no disturbance input
+
+      C = 0; D = 1; N_var = 0;
+
+
+      [PTcp1,PTcp2] = cosfil_ip(PTc,1); // PTc/1
+
+      [Fp1,Fp2] = cosfil_ip(1,F); // 1/F
+
+      [Ep,Fp] = cosfil_ip(E,F); // E/F
+
+      [PScp1,PScp2] = cosfil_ip(PSc,1); // PSc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 656
+  pk: 35
   fields:
     save_id: gallery34
     name: Ex9_19
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.19) Demonstration of usefulness of negative PID parameters'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="g_s_cl"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -54844,14 +66944,1866 @@
       as="geometry" height="40.0" width="100.0" x="450.0" y="420.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-7dc40e71:146d783a328:-7fa0" parent="-7dc40e71:146d783a328:-7f9f"/></XcosDiagram>
     media: gallery34.png
+    script_dump: '// Demonstration of usefulness of negative PID parameters, discussed
+      in Example 9.17 on page 361.
+
+      // 9.19
+
+      funcprot(0)
+
+      function Hd=iodelay(H,d)
+
+      if or(size(H.num)<>size(d)) then error(''Dimension mismatch''),end
+
+      Hd=mlist([''rd'',''H'',''iodelay''],H,d)
+
+      endfunction
+
+
+      //element wise product  overloading functions
+
+      function H=%rd_x_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H.*H2.H,H1.iodelay+ H2.iodelay)
+
+      endfunction
+
+      function H=%rd_x_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H.*H2,H1.iodelay)
+
+      endfunction
+
+      function H=%r_x_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.*H2.H,H2.iodelay)
+
+      endfunction
+
+      function H=%rd_x_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H.*H2,H1.iodelay)
+
+      endfunction
+
+      function H=%s_x_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.*H2.H,H2.iodelay)
+
+      endfunction
+
+
+      //column concatenation  overloading functions
+
+      function H=%rd_c_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H H2.H],[H1.iodelay,H2.iodelay])
+
+      endfunction
+
+      function H=%rd_c_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+
+      endfunction
+
+      function H=%r_c_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+
+      endfunction
+
+      function H=%rd_c_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H H2],[H1.iodelay,zeros(H2.num)])
+
+      endfunction
+
+      function H=%s_c_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1 H2.H],[zeros(H1.num),H2.iodelay])
+
+      endfunction
+
+
+      //row concatenation  overloading functions
+
+      function H=%rd_f_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H;H2.H],[H1.iodelay;H2.iodelay])
+
+      endfunction
+
+      function H=%rd_f_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+
+      endfunction
+
+      function H=%r_f_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+
+      endfunction
+
+      function H=%rd_f_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1.H;H2],[H1.iodelay;zeros(H2.num)])
+
+      endfunction
+
+      function H=%s_f_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=mlist([''rd'',''H'',''iodelay''],[H1;H2.H],[zeros(H1.num);H2.iodelay])
+
+      endfunction
+
+
+      //matrix product  overloading functions
+
+      function H=%rd_m_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      D2=H2.iodelay
+
+      D=D1*D2;
+
+      for k=1;size(D2,2)
+
+      for l=1:size(D1,1)
+
+      d=D1(l,:)+(D2(:,k)'')
+
+      if or(d(1)<>d) then error(''Delays mismatched''),end
+
+      D(l,k)=d
+
+      end
+
+      end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H*H2.H,D)
+
+      endfunction
+
+      function H=%rd_m_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      for l=1:size(D1,1)
+
+      if or(D1(l,1)<>D1(l,:)) then error(''Delays mismatched''),end
+
+      end
+
+      H=mlist([''rd'','''',''iodelay''],H1.H*H2,D1)
+
+      endfunction
+
+      function H=%rd_m_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      for l=1:size(D1,1)
+
+      if or(D1(l,1)<>D1(l,:)) then error(''Delays mismatched''),end
+
+      end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H*H2,D1)
+
+      endfunction
+
+      function H=%r_m_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D2=H2.iodelay
+
+      for l=1:size(D2,2)
+
+      if or(D2(1,l)<>D2(:,l)) then error(''Delays mismatched''),end
+
+      end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1*H2.H,D2)
+
+      endfunction
+
+      function H=%s_m_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D2=H2.iodelay
+
+      for l=1:size(D2,2)
+
+      if or(D2(1,l)<>D2(:,l)) then error(''Delays mismatched''),end
+
+      end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1*H2.H,D2)
+
+      endfunction
+
+
+      //Addition  overloading functions
+
+      function H=%rd_a_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      D2=H2.iodelay
+
+      if or(D1<>D2) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H+H2.H,D1)
+
+      endfunction
+
+      function H=%rd_a_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      if or(D1<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H+H2,D1)
+
+      endfunction
+
+      function H=%rd_a_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      if or(D1<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H+H2,D1)
+
+      endfunction
+
+      function H=%r_a_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D2=H2.iodelay
+
+      if or(D2<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1+H2.H,D2)
+
+      endfunction
+
+
+      //Substraction  overloading functions
+
+      function H=%rd_a_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      D2=H2.iodelay
+
+      if or(D1<>D2) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H-H2.H,D1)
+
+      endfunction
+
+      function H=%rd_a_r(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      if or(D1<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H-H2,D1)
+
+      endfunction
+
+      function H=%rd_a_s(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D1=H1.iodelay
+
+      if or(D1<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1.H-H2,D1)
+
+      endfunction
+
+      function H=%r_a_rd(H1,H2)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      D2=H2.iodelay
+
+      if or(D2<>0) then error(''Delay mismatch''),end
+
+      H=mlist([''rd'',''H'',''iodelay''],H1-H2.H,D2)
+
+      endfunction
+
+
+      //extraction  overloading functions
+
+      function H=%rd_e(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin($)
+
+      Hh= H.H;Hh.num=Hh.num(varargin(1:$-1));Hh.den=Hh.den(varargin(1:$-1));
+
+      H.H=Hh
+
+      H.iodelay=H.iodelay(varargin(1:$-1))
+
+      endfunction
+
+
+      //insertion  overloading functions
+
+      function H=%rd_i_rd(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin($)
+
+      Hfrom=varargin($-1)
+
+
+      Hh= H.H
+
+      Hh.num(varargin(1:$-2))=Hfrom.H.num
+
+      Hh.den(varargin(1:$-2))=Hfrom.H.den
+
+      H.H=Hh
+
+      H.iodelay(varargin(1:$-2))=Hfrom.iodelay
+
+      endfunction
+
+      function H=%r_i_rd(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin($)
+
+      Hfrom=varargin($-1)
+
+
+      Hh= H.H
+
+      Hh.num(varargin(1:$-2))=Hfrom.num
+
+      Hh.den(varargin(1:$-2))=Hfrom.den
+
+      H.H=Hh
+
+      H.iodelay(varargin(1:$-2))=zeros(Hfrom.num)
+
+      endfunction
+
+      function H=%s_i_rd(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin($)
+
+      Hfrom=varargin($-1)
+
+
+      Hh= H.H
+
+      Hh.num(varargin(1:$-2))=Hfrom
+
+      Hh.den(varargin(1:$-2))=ones(Hfrom)
+
+      H.H=Hh
+
+      H.iodelay(varargin(1:$-2))=zeros(Hfrom)
+
+      endfunction
+
+      function H=%rd_i_r(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      Hh=varargin($)
+
+      Hfrom=varargin($-1)
+
+      Hh.num(varargin(1:$-2))=Hfrom.H.num
+
+      Hh.den(varargin(1:$-2))=Hfrom.H.den
+
+      D=zeros(Hh.num)
+
+      D(varargin(1:$-2))=Hfrom.iodelay
+
+      H=mlist([''rd'',''H'',''iodelay''],Hh,D)
+
+      endfunction
+
+      function H=%rd_i_s(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      num=varargin($);den=ones(num)
+
+      Hfrom=varargin($-1)
+
+
+      num(varargin(1:$-2))=Hfrom.H.num
+
+      den(varargin(1:$-2))=Hfrom.H.den
+
+      D=zeros(num)
+
+      D(varargin(1:$-2))=Hfrom.iodelay
+
+      H=mlist([''rd'',''H'',''iodelay''],rlist(num,den,''c''),D)
+
+      endfunction
+
+
+      //transpostion  overloading function
+
+      function H=%rd_t(H)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H.H=H.H''
+
+      H.iodelay=H.iodelay''
+
+      endfunction
+
+
+      //string overloading function
+
+      function txt=%rd_string(H)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      r=H.H
+
+      N=string(r.num)
+
+      D=string(r.den)
+
+      ln=max(matrix(length(N),2,-1),''r'')
+
+      ld=max(matrix(length(D),2,-1),''r'')
+
+      l=max(ln,ld)
+
+      [m,n]=size(r.num);
+
+      S=emptystr(m,n)
+
+
+      kz=find(H.iodelay==0);//zero delay entries
+
+      w=''exp(''+string(-H.iodelay)+''*s)*'';w(kz)='''';
+
+
+      for i=1:m*n
+
+      s=2*i-1:2*i
+
+      pw=part('' '',1:length(w(i)))
+
+      N(s)=pw+part('' '',1:(l(i)-ln(i))/2)+N(s)
+
+      D(s)=pw+part('' '',1:(l(i)-ld(i))/2)+D(s)
+
+      S(i) =w(i)+part(''-'',ones(1,l(i)))
+
+      end
+
+      txt=emptystr(5*m,n);
+
+      txt(1:5:$,:)=N(1:2:$,:)
+
+      txt(2:5:$,:)=N(2:2:$,:)
+
+      txt(3:5:$,:)=S(1:$,:)
+
+      txt(4:5:$,:)=D(1:2:$,:)
+
+      txt(5:5:$,:)=D(2:2:$,:)
+
+      endfunction
+
+
+
+      //Display  overloading function
+
+      function %rd_p(H)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      //used to display rational fraction with complex coefficients
+
+      //The real case is hard coded
+
+      // Copyright INRIA
+
+      T=string(H)
+
+      l=max(length(T),''r'')
+
+      Te=emptystr(size(T,1),1)
+
+      for k=1:size(T,2)
+
+      Te=Te+part(T(:,k),1:l(k)+1)+''  ''
+
+      end
+
+      mprintf("%s\n",Te)
+
+      endfunction
+
+
+
+      //frequency response computation overloading
+
+      function [frq,repf,splitf]=repfreq(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin(1)
+
+      autolib.repfreq
+
+      if typeof(H)==''rd'' then
+
+      D=H.iodelay
+
+      varargin(1)=H.H
+
+      [frq,repf,splitf]=repfreq(varargin(:))
+
+
+      w=-2*%i*%pi*frq;
+
+      for k=1:size(D,''*'')
+
+      repf(k,:)=repf(k,:).*exp(D(k)*w)
+
+      end
+
+      else
+
+      [frq,repf,splitf]=repfreq(varargin(:))
+
+      end
+
+      endfunction
+
+
+      //bode plot computation overloading
+
+      function bode(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin(1)
+
+      xdesslib.bode
+
+      if typeof(H)==''rd'' then
+
+      if type(varargin($))==10 then //a comment
+
+      cm=varargin($);varagin($)=null()
+
+      else
+
+      cm=''''
+
+      end
+
+      D=H.iodelay
+
+      varargin(1)=H.H
+
+      [frq,repf,splitf]=repfreq(varargin(1:$))
+
+      w=-2*%i*%pi*frq;
+
+      for k=1:size(D,''*'')
+
+      repf(k,:)=repf(k,:).*exp(D(k)*w)
+
+      end
+
+      bode(frq,repf)
+
+      else
+
+      bode(varargin(:))
+
+      end
+
+      endfunction
+
+
+      //nyquist plot computation overloading
+
+      function nyquist(varargin)
+
+      // Author: Serge Steer, Copyright INRIA
+
+      H=varargin(1)
+
+      xdesslib.nyquist
+
+      if typeof(H)==''rd'' then
+
+      if type(varargin($))==10 then //a comment
+
+      cm=varargin($);varagin($)=null()
+
+      else
+
+      cm=''''
+
+      end
+
+      D=H.iodelay
+
+      varargin(1)=H.H
+
+      [frq,repf,splitf]=repfreq(varargin(1:$))
+
+      w=-2*%i*%pi*frq;
+
+      for k=1:size(D,''*'')
+
+      repf(k,:)=repf(k,:).*exp(D(k)*w)
+
+      end
+
+      nyquist(frq,repf)
+
+      else
+
+      nyquist(varargin(:))
+
+      end
+
+      endfunction
+
+
+      // Discretizing a tf with delay
+
+      // Exact solution
+
+      // Applicable for a 1st order system
+
+
+      // Ref.: pg.287,Digital Control,Prof.Kannan Moudgalya
+
+
+      // D: Delay
+
+      // TF:  e^(-Ds)       OR       e^(-Ds)
+
+      //    ------------          ------------  (gen.)
+
+      //     tau*s + 1              tau*s + a
+
+
+      //D = kTs + D'' (gen.)
+
+      // G: TF with delay component
+
+      // G1: TF with zero delay
+
+      // Required because G cannot be directly used in Scilab
+
+      // Coefficients are returned for ascending powers of z^-1
+
+
+      function [B,A,k1] = delc2d(G,G1,Ts)
+
+      D = G.iodelay;
+
+      d = coeff(G1(''den''));
+
+      if d(1) == 1
+
+      tau = d(2);
+
+      mu = 1;
+
+      else
+
+      tau = d(2)/d(1);
+
+      mu = 1/d(1);
+
+      end;
+
+
+      k = floor(D/Ts);
+
+      Dpri = D - k*Ts;
+
+      Dis = ((%z*(1 - (exp(-(Ts - Dpri)/tau)) ) )+ (exp(-(Ts - Dpri)/tau) - exp(-Ts/tau)
+      ))/ ((%z^(k+1))*(%z - exp(-Ts/tau)))
+
+      Dis1 = Dis*mu;
+
+      disp(''Warning: Exact discretization of first order system only'');
+
+      k1 = degree(Dis1(''den'')) - degree(Dis1(''num''));
+
+      B = coeff(Dis1(''num''));
+
+      A = coeff(Dis1(''den''));
+
+      B = flip(B);
+
+      A = flip(A);
+
+      endfunction;
+
+
+
+
+
+
+
+
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Solution to Aryabhatta''s identity arising in PID controller design, namely
+      Eq. 9.37 on page 363.
+
+      // 9.20
+
+
+      function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      dB = length(B) - 1; dA = length(A) - 1;
+
+      [zk,dzk] = zpowk(k);
+
+      [N,dN] = polmul(B,dB,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(A,dA,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+      [Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+
+      Rc = convol(R,Delta);
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      //User defined function
+
+      //Forms a transfer function
+
+      //Scilab: Co efficients are given in increasing power of variable
+
+      //Matlab: Co efficients are given in decreasing power of variable
+
+      //Hence co efficients are flipped here
+
+
+      //Input arguments: (1) Numerator co efficients(decreasing order)
+
+      //(2) Denominator co efficients
+
+      //(3) Variable to specify domain
+
+
+      // Updated (30-11-06)
+
+      // System is continuous => a is not passed
+
+      // System is discrete => a = -1
+
+      // System is discretized (sampled system) => a = Ts
+
+      // Uses syslin
+
+
+      function trfu = tf(num,den,a)
+
+      if argn(2) == 2
+
+      d = ''c'';
+
+      elseif a == -1
+
+      d = ''d'';
+
+      else
+
+      d = a
+
+      end;
+
+      num = clean(num);
+
+      den = clean(den);
+
+      num1 = poly(num(length(num):-1:1),''x'',''coeff'');
+
+      den1 = poly(den(length(den):-1:1),''x'',''coeff'');
+
+      trfu = syslin(d,num1,den1);
+
+      endfunction;
+
+
+
+
+      // 10.5
+
+      function b = flip(a)
+
+      b = a(length(a):-1:1);
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Discretize the continuous plant
+
+      num = 1; den = [2 1]; tau = 0.5;
+
+      G1 = tf(num,den);
+
+      G = iodelay(G1,tau);
+
+      Ts = 0.5;
+
+      [B,A,k] = delc2d(G,G1,Ts);
+
+
+      // Specify transient requirements
+
+      epsilon = 0.05; rise = 5;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Design the controller
+
+      Delta = [1 -1];
+
+      [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+
+      // parameters for simulation using g_s_cl
+
+      Tc = Sc; gamm = 1; N = 1;
+
+      C = 0; D = 1; N_var = 0;
+
+      st = 1; t_init = 0; t_final = 20;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+      Num = numer(G1);
+
+      Den = denom(G1);'
 - model: saveAPI.gallery
-  pk: 657
+  pk: 36
   fields:
     save_id: gallery35
     name: Ex9_1_1
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.1) Pole placement controller for magnetically suspended ball problem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="basic"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -57029,14 +70981,1171 @@
       as="geometry" height="40.0" width="50.0" x="530.0" y="290.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-64ce6d85:145ef6f2b4f:-7f9f" parent="-64ce6d85:145ef6f2b4f:-7f9e"/></XcosDiagram>
     media: gallery35.png
+    script_dump: '// Pole placement controller for magnetically suspended ball problem,
+      discussed in Example 9.3 on page 331.
+
+      // 9.1
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.2.
+
+      // 9.3
+
+      // function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors.
+
+      // Input is a polynomial in increasing degree of z^{-1}
+
+      // Optional input is a, where a <= 1.
+
+      // Factor that has roots of z^{-1} outside a is called
+
+      // good and the rest bad.
+
+      // If a is not specified, it will be assumed as 1-1.0e-5
+
+
+      function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      if argn(2) == 1, a = 1-1.0e-5; end
+
+      if a>1 error(''good polynomial is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts1 = roots(fac1);
+
+      rts = rts1(length(rts1):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = find(abs(rts)>=a); // mtlb_find has been replaced by find
+
+      badpoly = coeff(poly((rts(badindex)),"z","roots"));
+
+      goodindex = find(abs(rts)<a); // mtlb_find has been replaced by find
+
+      goodpoly = coeff(poly(rts(goodindex),"z","roots"));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad1 = goodbad(length(goodbad):-1:1);//--
+
+      factor1 = fac(index)/goodbad1(index);//--
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // Design of 2-DOF pole placement controller, as discussed in Sec. 9.2.
+
+      // 9.5
+
+
+      // function [Rc,Sc,Tc,gamma] = pp_basic(B,A,k,phi)
+
+      // calculates pole placement controller
+
+
+
+      function [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit2(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit2(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dphi = length(phi) - 1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,Ab,dAb,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,R1); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Magnetically suspended ball problem
+
+      // Operating conditions
+
+      M = 0.05; L = 0.01; R = 1; K = 0.0001; g = 9.81;
+
+
+      //Equilibrium conditions
+
+      hs = 0.01; is = sqrt(M*g*hs/K);
+
+
+      // State space matrices
+
+      a21 = K*is^2/M/hs^2; a23 = - 2*K*is/M/hs; a33 = - R/L;
+
+      b3 = 1/L;
+
+      a1 = [0 1 0; a21 0 a23; 0 0 a33];
+
+      b1 = [0; 0; b3]; c1 = [1 0 0]; d1 = 0;
+
+
+      // Transfer functions
+
+      G = syslin(''c'',a1,b1,c1,d1); Ts = 0.01;
+
+      [B,A,k] = myc2d(G,Ts);
+
+
+      //polynomials are returned
+
+      [Ds,num,den] = ss2tf(G);
+
+      num = clean(num); den = clean(den);
+
+
+      // Transient specifications
+
+      rise = 0.15; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+
+      // Setting up simulation parameters for basic.xcos
+
+      st = 0.0001; // desired change in h, in m.
+
+      t_init = 0; // simulation start time
+
+      t_final = 0.5; // simulation end time
+
+
+      // Setting up simulation parameters for c_ss_cl.xcos
+
+      N_var = 0; xInitial = [0 0 0]; N = 1; C = 0; D = 1;
+
+
+      [Tc1,Rc1] = cosfil_ip(Tc,Rc); // Tc/Rc
+
+      [Sc2,Rc2] = cosfil_ip(Sc,Rc); // Sc/Rc
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 658
+  pk: 37
   fields:
     save_id: gallery36
     name: Ex9_1_2
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.1) Pole placement controller for magnetically suspended ball problem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="Ex9_1_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -59365,14 +74474,1171 @@
       as="geometry" height="40.0" width="60.0" x="560.0" y="230.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="3844e477:143914d2fde:-7fa0" parent="3844e477:143914d2fde:-7f9f"/></XcosDiagram>
     media: gallery36.png
+    script_dump: '// Pole placement controller for magnetically suspended ball problem,
+      discussed in Example 9.3 on page 331.
+
+      // 9.1
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.2.
+
+      // 9.3
+
+      // function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors.
+
+      // Input is a polynomial in increasing degree of z^{-1}
+
+      // Optional input is a, where a <= 1.
+
+      // Factor that has roots of z^{-1} outside a is called
+
+      // good and the rest bad.
+
+      // If a is not specified, it will be assumed as 1-1.0e-5
+
+
+      function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      if argn(2) == 1, a = 1-1.0e-5; end
+
+      if a>1 error(''good polynomial is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts1 = roots(fac1);
+
+      rts = rts1(length(rts1):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = find(abs(rts)>=a); // mtlb_find has been replaced by find
+
+      badpoly = coeff(poly((rts(badindex)),"z","roots"));
+
+      goodindex = find(abs(rts)<a); // mtlb_find has been replaced by find
+
+      goodpoly = coeff(poly(rts(goodindex),"z","roots"));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad1 = goodbad(length(goodbad):-1:1);//--
+
+      factor1 = fac(index)/goodbad1(index);//--
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // Design of 2-DOF pole placement controller, as discussed in Sec. 9.2.
+
+      // 9.5
+
+
+      // function [Rc,Sc,Tc,gamma] = pp_basic(B,A,k,phi)
+
+      // calculates pole placement controller
+
+
+
+      function [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit2(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit2(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dphi = length(phi) - 1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,Ab,dAb,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,R1); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Magnetically suspended ball problem
+
+      // Operating conditions
+
+      M = 0.05; L = 0.01; R = 1; K = 0.0001; g = 9.81;
+
+
+      //Equilibrium conditions
+
+      hs = 0.01; is = sqrt(M*g*hs/K);
+
+
+      // State space matrices
+
+      a21 = K*is^2/M/hs^2; a23 = - 2*K*is/M/hs; a33 = - R/L;
+
+      b3 = 1/L;
+
+      a1 = [0 1 0; a21 0 a23; 0 0 a33];
+
+      b1 = [0; 0; b3]; c1 = [1 0 0]; d1 = 0;
+
+
+      // Transfer functions
+
+      G = syslin(''c'',a1,b1,c1,d1); Ts = 0.01;
+
+      [B,A,k] = myc2d(G,Ts);
+
+
+      //polynomials are returned
+
+      [Ds,num,den] = ss2tf(G);
+
+      num = clean(num); den = clean(den);
+
+
+      // Transient specifications
+
+      rise = 0.15; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+
+      // Setting up simulation parameters for basic.xcos
+
+      st = 0.0001; // desired change in h, in m.
+
+      t_init = 0; // simulation start time
+
+      t_final = 0.5; // simulation end time
+
+
+      // Setting up simulation parameters for c_ss_cl.xcos
+
+      N_var = 0; xInitial = [0 0 0]; N = 1; C = 0; D = 1;
+
+
+      [Tc1,Rc1] = cosfil_ip(Tc,Rc); // Tc/Rc
+
+      [Sc2,Rc2] = cosfil_ip(Sc,Rc); // Sc/Rc
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 659
+  pk: 38
   fields:
     save_id: gallery37
     name: Ex9_21_1
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.21) DC motor with PID control tuned through pole placement technique'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="Ex9_21_1"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -61920,14 +78186,1121 @@
       as="geometry" height="40.0" width="40.0" x="460.0" y="360.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-75a601dc:14604d880d0:-7ffd" parent="-75a601dc:14604d880d0:-7ffc"/></XcosDiagram>
     media: gallery37.png
+    script_dump: '// DC motor with PID control, tuned through pole placement technique,
+      as in Example 9.18.
+
+      // 9.21
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Solution to Aryabhatta''s identity arising in PID controller design, namely
+      Eq. 9.37 on page 363.
+
+      // 9.20
+
+
+      function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      dB = length(B) - 1; dA = length(A) - 1;
+
+      [zk,dzk] = zpowk(k);
+
+      [N,dN] = polmul(B,dB,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(A,dA,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+      [Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+
+      Rc = convol(R,Delta);
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // PD control law from polynomial coefficients, as explained in Sec. 9.8.
+
+      // 9.22
+
+
+      function [K,taud,N] = pd(Rc,Sc,Ts)
+
+
+      // Both Rc and Sc have to be degree one polynomials
+
+
+      s0 = Sc(1); s1 = Sc(2);
+
+      r1 = Rc(2);
+
+      K = (s0+s1)/(1+r1);
+
+      N = (s1-s0*r1)/r1/(s0+s1);
+
+      taudbyN = -Ts*r1/(1+r1);
+
+      taud = taudbyN * N;
+
+      endfunction;
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Motor control problem
+
+      // Transfer function
+
+
+      a = [-1 0; 1 0]; b = [1; 0]; c = [0 1]; d = 0;
+
+      G = syslin(''c'',a,b,c,d); Ts = 0.25;
+
+      [B,A,k] = myc2d(G,Ts);
+
+      [Ds,num,den] = ss2tf(G);
+
+
+      // Transient specifications
+
+      rise = 3; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = 1;  //No internal model of step used
+
+      [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+
+      // continuous time controller
+
+      [K,taud,N] = pd(Rc,Sc,Ts);
+
+      numb = K*[1 taud*(1+1/N)]; denb = [1 taud/N];
+
+      numf = 1; denf = 1;
+
+
+      // simulation parameters
+
+      st = 1;  // desired change in position
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+      st1 = 0;
+
+
+      // continuous controller simulation: g_s_cl3.xcos
+
+      num1 = 0; den1 = 1;
+
+
+      // discrete controller simulation: g_s_cl2.xcos
+
+      // u1: -0.1 to 0.8
+
+      // y1: 0 to 1.4
+
+      C = 0; D = 1; N = 1; gamm = 1; Tc = Sc;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+      Numb = polyno(numb,''s'');
+
+      Denb = polyno(denb,''s'');
+
+      Numf = polyno(numf,''s'');
+
+      Denf = polyno(denf,''s'');
+
+      Num1 = polyno(num1,''s'');
+
+      Den1 = polyno(den1,''s'');'
 - model: saveAPI.gallery
-  pk: 660
+  pk: 39
   fields:
     save_id: gallery38
     name: Ex9_21_2
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.21) DC motor with PID control tuned through pole placement technique'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="Ex9_21_2"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -64457,14 +81830,1121 @@
       x="540.0" y="210.0"/><mxPoint as="targetPoint" x="570.0" y="210.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="7b254bcc:14613988545:-7cfe" parent="7b254bcc:14613988545:-7cfd"/></XcosDiagram>
     media: gallery38.png
+    script_dump: '// DC motor with PID control, tuned through pole placement technique,
+      as in Example 9.18.
+
+      // 9.21
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Solution to Aryabhatta''s identity arising in PID controller design, namely
+      Eq. 9.37 on page 363.
+
+      // 9.20
+
+
+      function [Rc,Sc] = pp_pid(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      dB = length(B) - 1; dA = length(A) - 1;
+
+      [zk,dzk] = zpowk(k);
+
+      [N,dN] = polmul(B,dB,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(A,dA,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+      [Sc,dSc,R,dR] = xdync(N,dN,D,dD,phi,dphi);
+
+      Rc = convol(R,Delta);
+
+      endfunction;
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // PD control law from polynomial coefficients, as explained in Sec. 9.8.
+
+      // 9.22
+
+
+      function [K,taud,N] = pd(Rc,Sc,Ts)
+
+
+      // Both Rc and Sc have to be degree one polynomials
+
+
+      s0 = Sc(1); s1 = Sc(2);
+
+      r1 = Rc(2);
+
+      K = (s0+s1)/(1+r1);
+
+      N = (s1-s0*r1)/r1/(s0+s1);
+
+      taudbyN = -Ts*r1/(1+r1);
+
+      taud = taudbyN * N;
+
+      endfunction;
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // Motor control problem
+
+      // Transfer function
+
+
+      a = [-1 0; 1 0]; b = [1; 0]; c = [0 1]; d = 0;
+
+      G = syslin(''c'',a,b,c,d); Ts = 0.25;
+
+      [B,A,k] = myc2d(G,Ts);
+
+      [Ds,num,den] = ss2tf(G);
+
+
+      // Transient specifications
+
+      rise = 3; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = 1;  //No internal model of step used
+
+      [Rc,Sc] = pp_pid(B,A,k,phi,Delta);
+
+
+      // continuous time controller
+
+      [K,taud,N] = pd(Rc,Sc,Ts);
+
+      numb = K*[1 taud*(1+1/N)]; denb = [1 taud/N];
+
+      numf = 1; denf = 1;
+
+
+      // simulation parameters
+
+      st = 1;  // desired change in position
+
+      t_init = 0; // simulation start time
+
+      t_final = 20; // simulation end time
+
+      st1 = 0;
+
+
+      // continuous controller simulation: g_s_cl3.xcos
+
+      num1 = 0; den1 = 1;
+
+
+      // discrete controller simulation: g_s_cl2.xcos
+
+      // u1: -0.1 to 0.8
+
+      // y1: 0 to 1.4
+
+      C = 0; D = 1; N = 1; gamm = 1; Tc = Sc;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // N/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+      Numb = polyno(numb,''s'');
+
+      Denb = polyno(denb,''s'');
+
+      Numf = polyno(numf,''s'');
+
+      Denf = polyno(denf,''s'');
+
+      Num1 = polyno(num1,''s'');
+
+      Den1 = polyno(den1,''s'');'
 - model: saveAPI.gallery
-  pk: 661
+  pk: 40
   fields:
     save_id: gallery39
     name: basic_disc
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.7) Simulation of closed loop system with an unstable controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="1000.0" title="basic_disc"><!--Xcos - 1.0 - scilab-5.5.2
@@ -66643,14 +85123,1179 @@
       scilabClass="ScilabList"><mxPoint x="750.0" y="290.0"/></Array></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-7476484f:145f8cd2a3c:-7f9e" parent="-7476484f:145f8cd2a3c:-7f9d"/></XcosDiagram>
     media: gallery39.png
+    script_dump: '// Simulation of closed loop system with an unstable controller,
+      as discussed in Example 9.5 on page 335.
+
+      // 9.7
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.2.
+
+      // 9.3
+
+      // function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors.
+
+      // Input is a polynomial in increasing degree of z^{-1}
+
+      // Optional input is a, where a <= 1.
+
+      // Factor that has roots of z^{-1} outside a is called
+
+      // good and the rest bad.
+
+      // If a is not specified, it will be assumed as 1-1.0e-5
+
+
+      function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      if argn(2) == 1, a = 1-1.0e-5; end
+
+      if a>1 error(''good polynomial is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts1 = roots(fac1);
+
+      rts = rts1(length(rts1):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = find(abs(rts)>=a); // mtlb_find has been replaced by find
+
+      badpoly = coeff(poly((rts(badindex)),"z","roots"));
+
+      goodindex = find(abs(rts)<a); // mtlb_find has been replaced by find
+
+      goodpoly = coeff(poly(rts(goodindex),"z","roots"));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad1 = goodbad(length(goodbad):-1:1);//--
+
+      factor1 = fac(index)/goodbad1(index);//--
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Design of 2-DOF pole placement controller, as discussed in Sec. 9.2.
+
+      // 9.5
+
+
+      // function [Rc,Sc,Tc,gamma] = pp_basic(B,A,k,phi)
+
+      // calculates pole placement controller
+
+
+
+      function [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit2(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit2(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dphi = length(phi) - 1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,Ab,dAb,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,R1); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      Ts = 1; B = [1 -3]; A = [1 2 -8]; k = 1;
+
+      // Since k=1, tf is of the form z^-1
+
+      [zk,dzk] = zpowk(k); // int1 = 0;//---- int1
+
+
+      // Transient specifications
+
+      rise = 10; epsilon = 0.1;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+
+      // simulation parameters for basic_disc.xcos
+
+      //While simulating for t_final = 100, set the limit of Y axis of each scope
+
+      //u1: -0.2 to 3
+
+      //y1: -0.1 to 1.2
+
+      st = 1.0; // Desired change in setpoint
+
+      t_init = 0; // Simulation start time
+
+      t_final = 1000; // Simulation end time
+
+
+      // Simulation parameters for stb_disc.xcos
+
+      N_var = 0; C = 0; D = 1; N = 1;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+      [Tcp,Rcp] = cosfil_ip(Tc,Rc); // Tc/Rc
+
+      [Scp_b,Rcp_b] = cosfil_ip(Sc,Rc); // Sc/Rc'
 - model: saveAPI.gallery
-  pk: 662
+  pk: 41
   fields:
     save_id: gallery40
     name: stb_disc
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.7) Simulation of closed loop system with an unstable controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="stb_disc"><!--Xcos - 1.0 - scilab-5.5.2 -
@@ -68994,15 +88639,1180 @@
       x="370.0" y="140.0"/></Array></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-7476484f:145f8cd2a3c:-7be9" parent="-7476484f:145f8cd2a3c:-7be8"/></XcosDiagram>
     media: gallery40.png
+    script_dump: '// Simulation of closed loop system with an unstable controller,
+      as discussed in Example 9.5 on page 335.
+
+      // 9.7
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.2.
+
+      // 9.3
+
+      // function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors.
+
+      // Input is a polynomial in increasing degree of z^{-1}
+
+      // Optional input is a, where a <= 1.
+
+      // Factor that has roots of z^{-1} outside a is called
+
+      // good and the rest bad.
+
+      // If a is not specified, it will be assumed as 1-1.0e-5
+
+
+      function [goodpoly,badpoly] = polsplit2(fac,a)
+
+      if argn(2) == 1, a = 1-1.0e-5; end
+
+      if a>1 error(''good polynomial is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts1 = roots(fac1);
+
+      rts = rts1(length(rts1):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = find(abs(rts)>=a); // mtlb_find has been replaced by find
+
+      badpoly = coeff(poly((rts(badindex)),"z","roots"));
+
+      goodindex = find(abs(rts)<a); // mtlb_find has been replaced by find
+
+      goodpoly = coeff(poly(rts(goodindex),"z","roots"));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad1 = goodbad(length(goodbad):-1:1);//--
+
+      factor1 = fac(index)/goodbad1(index);//--
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Design of 2-DOF pole placement controller, as discussed in Sec. 9.2.
+
+      // 9.5
+
+
+      // function [Rc,Sc,Tc,gamma] = pp_basic(B,A,k,phi)
+
+      // calculates pole placement controller
+
+
+
+      function [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit2(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit2(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dphi = length(phi) - 1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,Ab,dAb,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,R1); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+
+      Ts = 1; B = [1 -3]; A = [1 2 -8]; k = 1;
+
+      // Since k=1, tf is of the form z^-1
+
+      [zk,dzk] = zpowk(k); // int1 = 0;//---- int1
+
+
+      // Transient specifications
+
+      rise = 10; epsilon = 0.1;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      [Rc,Sc,Tc,gamm] = pp_basic(B,A,k,phi);
+
+
+      // simulation parameters for basic_disc.xcos
+
+      //While simulating for t_final = 100, set the limit of Y axis of each scope
+
+      //u1: -0.2 to 3
+
+      //y1: -0.1 to 1.2
+
+      st = 1.0; // Desired change in setpoint
+
+      t_init = 0; // Simulation start time
+
+      t_final = 1000; // Simulation end time
+
+
+      // Simulation parameters for stb_disc.xcos
+
+      N_var = 0; C = 0; D = 1; N = 1;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Rcp1,Rcp2] = cosfil_ip(1,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Bp,Ap] = cosfil_ip(B,A); // B/A
+
+      [zkp1,zkp2] = cosfil_ip(zk,1); // zk/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D
+
+
+      [Tcp,Rcp] = cosfil_ip(Tc,Rc); // Tc/Rc
+
+      [Scp_b,Rcp_b] = cosfil_ip(Sc,Rc); // Sc/Rc'
 - model: saveAPI.gallery
-  pk: 663
+  pk: 42
   fields:
     save_id: gallery41
     name: Ex9_9
     description: 'Digital Control (Author: K. M. Moudgalya), 9) Pole Placement Controllers,
       9.9) Pole placement controller with internal model of a step for the magnetically
       suspended ball problem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2048
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="Ex9_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20150331
@@ -71289,15 +92099,1157 @@
       x="510.0" y="340.0"/><Array as="points" scilabClass=""><mxPoint x="510.0" y="440.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="3af18dde:16fc1cf9366:-7cf3" parent="3af18dde:16fc1cf9366:-7cf2"/></XcosDiagram>
     media: gallery41.png
+    script_dump: '// Pole placement controller, with internal model of a step, for
+      the magnetically suspended ball problem, as discussed in Example 9.8 on page
+      339.
+
+      // 9.9
+
+      // Calculation of desired closed loop characteristic polynomial, as discussed
+      in Sec. 7.7.
+
+      // 9.4
+
+
+      // function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      // Based on transient requirements,
+
+      // calculates closed loop characteristic polynomial
+
+
+      function [phi,dphi] = desired(Ts,rise,epsilon)
+
+      Nr = rise/Ts; omega = %pi/2/Nr; rho = epsilon^(omega/%pi);
+
+      phi = [1 -2*rho*cos(omega) rho^2]; dphi = length(phi)-1;
+
+      endfunction;
+
+      // Pole placement controller using internal model principle, as discussed in
+      Sec. 9.4.
+
+      // 9.8
+
+
+      // function [Rc,Sc,Tc,gamma,phit] = pp_im(B,A,k,phi,Delta)
+
+      // Calculates 2-DOF pole placement controller.
+
+
+      function [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta)
+
+
+      // Setting up and solving Aryabhatta identity
+
+      [Ag,Ab] = polsplit3(A); dAb = length(Ab) - 1;
+
+      [Bg,Bb] = polsplit3(B); dBb = length(Bb) - 1;
+
+
+      [zk,dzk] = zpowk(k);
+
+
+      [N,dN] = polmul(Bb,dBb,zk,dzk);
+
+      dDelta = length(Delta)-1;
+
+      [D,dD] = polmul(Ab,dAb,Delta,dDelta);
+
+      dphi = length(phi)-1;
+
+
+      [S1,dS1,R1,dR1] = xdync(N,dN,D,dD,phi,dphi);
+
+
+      // Determination of control law
+
+      Rc = convol(Bg,convol(R1,Delta)); Sc = convol(Ag,S1);
+
+      Tc = Ag; gamm = sum(phi)/sum(Bb);
+
+      endfunction;
+
+      // Discretization of continuous transfer function. The result is numerator and
+      denominator in powers of z^{-1} and the delay term k.
+
+      // 9.2
+
+      // function [B,A,k] = myc2d(G,Ts)
+
+      // Produces numerator and denominator of discrete transfer
+
+      // function in powers of z^{-1}
+
+      // G is continuous transfer function; time delays are not allowed
+
+      // Ts is the sampling time, all in consistent time units
+
+
+      function [B,A,k] = myc2d(G,Ts)
+
+      H = ss2tf(dscr(G,Ts));
+
+      num1 = coeff(H(''num''));
+
+      den1 = coeff(H(''den''));//-------------
+
+      A = den1(length(den1):-1:1);
+
+      num2 = num1(length(num1):-1:1);  //flip
+
+      nonzero = find(num1);
+
+      first_nz = nonzero(1);
+
+      B = num2(first_nz:length(num2)); //-------------
+
+      k = length(den1) - length(num1);
+
+      endfunction
+
+
+      // Procedure to split a polynomial into good and bad factors, as discussed in
+      Sec. 9.5. The factors that have roots outside unit circle or with negative real
+      parts are defined as bad.
+
+      // 9.12
+
+
+      // function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      // Splits a scalar polynomial of z^{-1} into good and bad
+
+      // factors. Input is a polynomial in increasing degree of
+
+      // z^{-1}.  Optional input is a, where a <= 1.
+
+      // Factors that have roots outside a circle of radius a or
+
+      // with negative roots will be called bad and the rest
+
+      // good. If a is not specified, it will be assumed as 1.
+
+
+      function [goodpoly,badpoly] = polsplit3(fac,a)
+
+      if argn(2) == 1, a = 1; end
+
+      if a>1 error(''good polynomial also is unstable''); end
+
+      fac1 = poly(fac(length(fac):-1:1),''z'',''coeff'');
+
+      rts = roots(fac1);
+
+      rts = rts(length(rts):-1:1);
+
+
+      // extract good and bad roots
+
+      badindex = mtlb_find((abs(rts)>=a-1.0e-5)|(real(rts)<-0.05));
+
+      badpoly = coeff(poly(rts(badindex),''z''));
+
+      goodindex = mtlb_find((abs(rts)<a-1.0e-5)&(real(rts)>=-0.05));
+
+      goodpoly = coeff(poly(rts(goodindex),''z''));
+
+
+      // scale by equating the largest terms
+
+      [m,index] = max(abs(fac));
+
+      goodbad = convol(goodpoly,badpoly);
+
+      goodbad = goodbad(length(goodbad):-1:1);
+
+      factor1 = fac(index)/goodbad(index);
+
+      goodpoly = goodpoly * factor1;
+
+      goodpoly = goodpoly(length(goodpoly):-1:1);
+
+      badpoly = badpoly(length(badpoly):-1:1);
+
+      endfunction;
+
+      // Evaluates z^-k.
+
+      // 9.6
+
+
+      function [zk,dzk] = zpowk(k)
+
+      zk = zeros(1,k+1); zk(1,k+1) = 1;
+
+      dzk = k;
+
+      endfunction
+
+      // function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+      // MATLAB FUNCTION rowjoin TO SUPERPOSE TWO POLYNOMIAL
+
+      // MATRICES
+
+
+      // H. Kwakernaak, July, 1990
+
+
+      function [P,degP] = rowjoin(P1,degP1,P2,degP2)
+
+
+      [rP1,cP1] = polsize(P1,degP1);
+
+      [rP2,cP2] = polsize(P2,degP2);
+
+      if cP1 ~= cP2
+
+      error(''rowjoin: Inconsistent numbers of columns'');
+
+      end
+
+
+      rP = rP1+rP2; cP = cP1;
+
+      if degP1 >= degP2
+
+      degP = degP1;
+
+      else
+
+      degP = degP2;
+
+      end
+
+
+      if isempty(P1)
+
+      P = P2;
+
+      elseif isempty(P2)
+
+      P = P1;
+
+      else
+
+      P = zeros(rP,(degP+1)*cP);
+
+      P(1:rP1,1:(degP1+1)*cP1) = P1;
+
+      P(rP1+1:rP,1:(degP2+1)*cP2) = P2;
+
+      end
+
+      endfunction
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = ...
+
+      // left_prm(N,degN,D,degD,job,gap)
+
+      //
+
+      // does three different things according to integers that ''job'' takes
+
+      // job = 1.
+
+      // this is the default.  It is always done for all jobs.
+
+      //         -1                                  -1    -1
+
+      // Given ND  , returns coprime B and A where ND   = A  B
+
+      // It is enough if one sends the first four input arguments
+
+      // If gap is required to be sent, then one can send either 1 or a null
+
+      // entry for job
+
+      // job = 2.
+
+      // first solve for job = 1 and then solve XA + YB = I
+
+      // job = 3.
+
+      // used in solving XD + YN = C
+
+      // after finding coprime factorization, data are returned
+
+      //
+
+      // convention: the variable with prefix deg stand for degrees
+
+      // of the corresponding polynomial matrices
+
+      //
+
+      // input:
+
+      // N: right fraction numerator polynomial matrix
+
+      // D: right fraction denominator polynomial matrix
+
+      // N and D are not neccessarily coprime
+
+      // gap: variable used to zero entries; default value is 1.0e+8
+
+      //
+
+      // output
+
+      // b and A are left  coprime num. and den. polynomial matrices
+
+      // X and Y are solutions to Aryabhatta identity, only for job = 2
+
+
+      function [B,degB,A,degA,Y,degY,X,degX] = left_prm(N,degN,D,degD,job,gap)
+
+      if argn(2) == 4 | argn(2) == 5
+
+      gap = 1.0e8 ;
+
+      end
+
+      // pause
+
+      if argn(2) == 4,
+
+      job = 1; end
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+      [Frows,Fbcols] = polsize(F,degF);       // Fbcols = block columns
+
+      Fcols = Fbcols * (degF+1) ;             // actual columns of F
+
+      T1 = [];pr =[];degT1 = 0; T1rows = 0;shft = 0;
+
+      S=F; sel = ones(Frows,1); T1bcols =1;
+
+      abar = (Fbcols + 1):Frows;              // a_super_bar of B-C.Chang
+
+      while isempty(T1) | T1rows < Frows - Fbcols
+
+      Srows = Frows*T1bcols; // max actual columns of result
+
+      [T1,T1rows,sel,pr] = ...
+
+      t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap);
+
+      [T1rows,T1cols] = size(T1);
+
+      if T1rows < Frows - Fbcols
+
+      T1 = [T1 zeros(T1rows,Frows)];
+
+      T1bcols = T1bcols  + 1;         // max. block columns of result
+
+      degT1 = degT1 + 1;              // degree of result
+
+      shft = shft +Fbcols;
+
+      S = seshft(S,F,shft);
+
+      sel = [sel;sel(Srows-Frows+1:Srows)];
+
+      rowvec = (T1bcols-1)*Frows+(Fbcols+1):T1bcols * Frows;
+
+      abar = [abar rowvec];           // A_super_bar of B-C.chang
+
+      end
+
+      end
+
+
+      [B,degB,A,degA] = colsplit(T1,degT1,Fbcols,Frows-Fbcols);
+
+      [B,degB] = clcoef(B,degB);
+
+      B = -B;
+
+      [A,degA] = clcoef(A,degA);
+
+      // pause
+
+      if job == 2
+
+      S = S(mtlb_logical(sel),:);                      // columns
+
+      [redSrows,Scols] = size(S);
+
+      C = [eye(Fbcols,Fbcols) zeros(Fbcols,Scols-Fbcols)];   // append with zeros
+
+      T2 = C/S;
+
+      T2 = makezero(T2,gap);
+
+      T2 = move_sci(T2,find(sel),Srows);
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows - Fbcols);
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      elseif job == 3
+
+      Y = S;
+
+      degY = sel;
+
+      X = degT1;
+
+      degX = Fbcols;
+
+      else
+
+      if job ~= 1
+
+      error(''Message from left_prm:no legal job number specified'')
+
+      end
+
+      end
+
+      endfunction
+
+
+
+
+      // function [T1,T1rows,sel,pr] = ...
+
+      // t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      // calculates the coefficient matrix T1
+
+      // redundant row information is kept in sel: redundant rows are marked
+
+      // with zeros.  The undeleted rows are marked with ones.
+
+
+      function [T1,T1rows,sel,pr] = t1calc(S,Srows,T1,T1rows,sel,pr,Frows,Fbcols,abar,gap)
+
+      b = 1;                                  // vector of primary red.rows
+
+
+      while (T1rows < Frows - Fbcols) & or(sel==1) & ~isempty(b)
+
+      S = clean(S);
+
+      b = indep(S(mtlb_logical(sel),:),gap); // send selected rows of S
+
+      if ~isempty(b)
+
+      b = clean(b);
+
+      b = move_sci(b,find(sel),Srows);
+
+      j = length(b);
+
+      while ~(b(j) & or(abar==j))   // pick largest nonzero entry
+
+      j = j-1;                // of coeff. belonging to abar
+
+      if ~j
+
+      fprintf(''\nMessage from t1calc, called from left_prm\n\n'')
+
+      error(''Denominator is noninvertible'')
+
+      end
+
+      end
+
+      if ~or(j<pr & pmodulo(pr,Frows) == pmodulo(j,Frows)) // pr(2),pr(1)
+
+      T1 = [T1; b];               // condition is not violated
+
+      T1rows = T1rows +1;         // accept this vector
+
+      end                            // else don''t accept
+
+      pr = [pr; j];                  // update prime red row info
+
+      while j <= Srows
+
+      sel(j) = 0;
+
+      j = j + Frows;
+
+      end
+
+      end
+
+      end
+
+      endfunction
+
+      // function b = indep(S,gap)
+
+      // determines the first row that is dependent on the previous rows of S.
+
+      // The coefficients of dependence is returned in b
+
+      function b = indep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      [rows,cols] = size(S);
+
+      ind = 1;
+
+      i = 2;
+
+      eps = 2.2204e-016;
+
+      while ind & i <= rows
+
+      sigma = svd(S(1:i,:));
+
+      len = length(sigma);
+
+      if(sigma(len)/sigma(1) < (eps*max(i,cols)))
+
+      ind =0;
+
+      else
+
+      shsig = [sigma(2:len);sigma(len)];
+
+      if or( (sigma ./shsig) > gap)
+
+      ind = 0;
+
+      else
+
+      ind = 1;
+
+      i = i+1;
+
+      end
+
+      end
+
+
+      end
+
+      if ind
+
+      b =[];
+
+
+      else
+
+      c = S(i,:)/S(1:i-1,:);
+
+      c = makezero(c,gap);
+
+      b = [-c 1];
+
+      end
+
+      endfunction
+
+
+      // function b = cindep( S,gap)
+
+      // Used in XD + YN = C. All rows except the last of are assumed to
+
+      // be independent.  The aim is to check if the last row is dependent on the
+
+      // rest and if so how.  The coefficients of dependence are sent in b.
+
+      function b = cindep( S,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      eps = 2.2204e-016;
+
+      [rows,cols] = size(S);
+
+      if rows > cols
+
+      ind = 0;
+
+      else
+
+      sigma = svd(S);
+
+      len = length(sigma);
+
+      if (sigma(len)/sigma(1) <= (eps*max(i,cols)))
+
+      ind = 0;                  //not independent
+
+      else
+
+      if or(sigma(1:len-1) ./sigma(2:len)>=gap)
+
+      ind = 0;               // not dependent
+
+      else
+
+      ind = 1;               //independent
+
+      end
+
+      end
+
+      end
+
+      if ind
+
+      b = [];
+
+      else
+
+      b = S(rows,:)/S(1:rows-1,:);
+
+      b = makezero(b,gap);
+
+      end
+
+      endfunction
+
+
+
+      // function C = seshft(A,B,N)
+
+      //given A and B matrices, returns C = [<-A-> 0
+
+      //                                    0  <-B->] with B shifted east by N cols
+
+
+      function C = seshft(A,B,N)
+
+      [Arows,Acols] = size(A);
+
+      [Brows,Bcols] = size(B);
+
+      if N >= 0
+
+      B = [zeros(Brows,N) B];
+
+      Bcols = Bcols + N;
+
+      elseif N < 0
+
+      A = [zeros(Arows,abs(N)) A];
+
+      Acols = Acols +abs(N);
+
+      end
+
+      if Acols < Bcols
+
+      A = [A zeros(Arows,Bcols-Acols)];
+
+      elseif Acols > Bcols
+
+      B = [B zeros(Brows,Acols-Bcols)];
+
+      end
+
+      C = [A
+
+      B];
+
+      endfunction
+
+      // function B = makezero(B,gap)
+
+      // where B is a vector and gap acts as a tolerance
+
+
+      function B = makezero(B,gap)
+
+
+      if argn(2) == 1
+
+      gap = 1.0e8;
+
+      end
+
+      temp = B(find(B));        // non zero entries of B
+
+      temp = -gsort(-abs(temp),''g'',''d''); // absolute values sorted in descending
+      order
+
+      len = length(temp);
+
+      ratio = temp(1:len-1) ./temp(2:len); // each ratio >1
+
+      min_ind = min(find(ratio>gap));
+
+      if ~isempty(min_ind)
+
+      our_eps = temp(min_ind+1);
+
+      zeroind = find(abs(B)<=our_eps);
+
+      B(zeroind) = zeros(1,length(zeroind));
+
+      end
+
+      endfunction
+
+      // function result = move_sci(b,nonred,max_sci)
+
+      // Moves matrix b to matrix result with the information on where to move,
+
+      // decided by the indices of nonred.
+
+      // The matrix result will have as many rows as b has and max number of columns.
+
+      // b is augumented with zeros to have nonred number of columns;
+
+      // The columns of b put into those of result as decided by nonred.
+
+
+      function result = move_sci(b,nonred,max_sci)
+
+      [brows,bcols] = size(b);
+
+      b = [b zeros(brows,length(nonred)-bcols)];
+
+      result = zeros(brows,max_sci);
+
+      result(:,nonred'') = b;
+
+      endfunction
+
+      // colsplit
+
+      // The command
+
+      //   [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+      // produces two polynomial matrix P1 and P2. P1 consists of the first
+
+      // p1 columns of P and P2 consists of the remaining p2 columns of P.
+
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [P1,degP1,P2,degP2] = colsplit(P,degP,p1,p2)
+
+
+      if isempty(P)
+
+      P1 = []; P2 = [];
+
+      degP1 = 0; degP2 = 0;
+
+      return;
+
+      end
+
+
+      [rP,cP] = polsize(P,degP);
+
+      if p1 < 0 | p1 > cP | p2 < 0 | p2 > cP | p1+p2 ~= cP
+
+      error(''colsplit: Inconsistent numbers of columns'');
+
+      end
+
+      rP1 = rP; rP2 = rP; cP1 = p1; cP2 = p2;
+
+      degP1= degP; degP2 = degP;
+
+
+      if p1 == 0
+
+      P1 == []; P2 = P;
+
+      elseif p2 == 0
+
+      P1 = P; P2 = [];
+
+      else
+
+      P1 = zeros(rP1,(degP1+1)*cP1); P2 = zeros(rP2,(degP2+1)*cP2);
+
+      for i = 1:degP+1
+
+      P1(:,(i-1)*cP1+1:i*cP1) = P(:,(i-1)*cP+1:(i-1)*cP+cP1);
+
+      P2(:,(i-1)*cP2+1:i*cP2) = P(:,(i-1)*cP+cP1+1:i*cP);
+
+      end
+
+      end
+
+      endfunction;
+
+      // H. Kwakernaak, July, 1990
+
+      // Modified by Kannan Moudgalya in Nov. 1992
+
+
+      function [P,degP] = clcoef(Q,degQ)
+
+
+      [rQ,cQ] = polsize(Q,degQ);
+
+
+      if and(and(Q==0))
+
+      P = zeros(rQ,cQ);
+
+      degP = 0;
+
+      else
+
+      P = Q; degP = degQ; rP = rQ; cP = cQ;
+
+      j = degP+1;
+
+      while j >= 0
+
+      X = P(:,(j-1)*cP+1:j*cP)
+
+      if max(sum(abs(X''))) < (1e-8)*max(sum(abs(P)))
+
+      P = P(:,1:(j-1)*cP);
+
+      degP = degP-1;
+
+      else
+
+      j = 0;
+
+      end
+
+      j = j-1;
+
+      end
+
+      end
+
+      endfunction
+
+      // polmul
+
+      // The command
+
+      //    [C,degA] = polmul(A,degA,B,degB)
+
+      // produces the polynomial matrix C that equals the product A*B of the
+
+      // polynomial matrices A and B.
+
+      //
+
+      // H. Kwakernaak, July, 1990
+
+
+
+      function [C,degC] = polmul(A,degA,B,degB)
+
+      [rA,cA] = polsize(A,degA);
+
+      [rB,cB] = polsize(B,degB);
+
+      if cA ~= rB
+
+      error(''polmul: Inconsistent dimensions of input matrices'');
+
+      end
+
+
+      degC = degA+degB;
+
+      C = [];
+
+      for k = 0:degA+degB
+
+      mi = 0;
+
+      if k-degB > mi
+
+      mi = k-degB;
+
+      end
+
+      ma = degA;
+
+      if k < ma
+
+      ma = k;
+
+      end
+
+      Ck = zeros(rA,cB);
+
+      for i = mi:ma
+
+      Ck = Ck + A(:,i*cA+1:(i+1)*cA)*B(:,(k-i)*cB+1:(k-i+1)*cB);
+
+      end
+
+      C = [C Ck];
+
+      end
+
+      endfunction
+
+      // function [rQ,cQ] = polsize(Q,degQ)
+
+      // FUNCTION polsize TO DETERMINE THE DIMENSIONS
+
+      // OF A POLYNOMIAL MATRIX
+
+      //
+
+      // H. Kwakernaak, August, 1990
+
+
+      function [rQ,cQ] = polsize(Q,degQ)
+
+
+      [rQ,cQ] = size(Q); cQ = cQ/(degQ+1);
+
+      if abs(round(cQ)-cQ) > 1e-6
+
+      error(''polsize: Degree of input inconsistent with number of columns'');
+
+      else
+
+      cQ = round(cQ);
+
+      end
+
+      endfunction
+
+      // function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      // given coefficient matrix in T1, primary redundant row information sel,
+
+      // solves XD + YN = C
+
+
+      // calling order changed on 16 April 2005.  Old order:
+
+      // function [B,degB,A,degA,Y,degY,X,degX] = xdync(N,degN,D,degD,C,degC,gap)
+
+
+      function [Y,degY,X,degX,B,degB,A,degA] = xdync(N,degN,D,degD,C,degC,gap)
+
+      if argn(2) == 6
+
+      gap = 1.0e+8;
+
+      end
+
+
+      [F,degF] = rowjoin(D,degD,N,degN);
+
+
+      [Frows,Fbcols] = polsize(F,degF); //Fbcols = block columns
+
+
+      [B,degB,A,degA,S,sel,degT1,Fbcols] = left_prm(N,degN,D,degD,3,gap);
+
+      //if issoln(D,degD,C,degC,B,degB,A,degA)
+
+      [Crows,Ccols] = size(C);
+
+      [Srows,Scols] = size(S);
+
+      S = clean(S);
+
+      S = S(mtlb_logical(sel),:);
+
+      T2 =[];
+
+
+      for i = 1:Crows,
+
+      Saug = seshft(S,C(i,:),0);
+
+      b = cindep(Saug);
+
+      b = move_sci(b,find(sel),Srows);
+
+      T2 =[T2; b];
+
+      end
+
+
+      [X,degX,Y,degY] = colsplit(T2,degT1,Fbcols,Frows-Fbcols);
+
+
+      [X,degX] = clcoef(X,degX);
+
+      [Y,degY] = clcoef(Y,degY);
+
+      Y = clean(Y); X = clean(X);
+
+      endfunction
+
+      // Input arguments are co efficients of numerator and denominator
+
+      // polynomials in ascending powers of z^-1
+
+
+      // Scicos/Xcos blocks need input polynomials
+
+      // with positive powers of z
+
+
+      function [nume,deno] = cosfil_ip(num,den)
+
+
+      [Nn,Nd] = polyno(num,''z'');
+
+      [Dn,Dd] = polyno(den,''z'');
+
+      nume = Nn*Dd;
+
+      deno = Nd*Dn;
+
+
+      endfunction;
+
+
+      // Updated(1-8-07)
+
+      // Operations:
+
+      // Polynomial definition
+
+      // Flipping of coefficients
+
+      // Variables ------- passed as input argument (either ''s'' or ''z'')
+
+      // Both num and den are used mostly used in scicos files,
+
+      // to get rid of negative powers of z
+
+
+      // Polynomials with powers of s need to
+
+      // be flipped only
+
+
+      function [polynu,polyde] = polyno(zc,a)
+
+      zc = clean(zc);
+
+      polynu = poly(zc(length(zc):-1:1),a,''coeff'');
+
+      if a == ''z''
+
+      polyde = %z^(length(zc) - 1);
+
+      else
+
+      polyde = 1;
+
+      end
+
+
+      // Scicos(4.1) Filter block shouldn''t have constant/constant
+
+      if type(polynu)==1 & type(polyde)==1
+
+      if a == ''z''
+
+      polynu = %z; polyde = %z;
+
+      else
+
+      polynu = %s; polyde = %s;
+
+      end;
+
+      end;
+
+
+      endfunction
+
+      // Operating conditions
+
+      M = 0.05; L = 0.01; R = 1; K = 0.0001; g = 9.81;
+
+
+      // Equilibrium conditions
+
+      hs = 0.01; is = sqrt(M*g*hs/K);
+
+
+      // State space matrices
+
+      a21 = K*is^2/M/hs^2; a23 = - 2*K*is/M/hs; a33 = - R/L;
+
+      b3 = 1/L;
+
+      a1 = [0 1 0; a21 0 a23; 0 0 a33];
+
+      b1 = [0; 0; b3]; c1 = [1 0 0]; d1 = 0;
+
+
+      // Transfer functions
+
+      G = syslin(''c'',a1,b1,c1,d1); Ts = 0.01; [B,A,k] = myc2d(G,Ts);
+
+
+      // Transient specifications
+
+      rise = 0.1; epsilon = 0.05;
+
+      phi = desired(Ts,rise,epsilon);
+
+
+      // Controller design
+
+      Delta = [1 -1];  //internal model of step used
+
+      [Rc,Sc,Tc,gamm] = pp_im(B,A,k,phi,Delta);
+
+
+      // simulation parameters for c_ss_cl.xcos
+
+      st = 0.0001;  //desired change in h, in m.
+
+      t_init = 0; // simulation start time
+
+      t_final = 0.5; //simulation end time
+
+      xInitial = [0 0 0];
+
+      N = 1; C = 0; D = 1; N_var = 0;
+
+
+      [Tcp1,Tcp2] = cosfil_ip(Tc,1); // Tc/1
+
+      [Np,Rcp] = cosfil_ip(N,Rc); // 1/Rc
+
+      [Scp1,Scp2] = cosfil_ip(Sc,1); // Sc/1
+
+      [Cp,Dp] = cosfil_ip(C,D); // C/D'
 - model: saveAPI.gallery
-  pk: 664
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   fields:
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     name: ex10_10
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.10) Superposition Source Transformations
       and Thevenin theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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 - model: saveAPI.gallery
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.11) Superposition Source Transformations
       and Thevenin theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
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 - model: saveAPI.gallery
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.1) Forced Response to sinusoidal
       functions'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     name: ex10_6
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.6) Impedance'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
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 - model: saveAPI.gallery
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     name: ex10_7
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.7) Nodal and Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.8) Nodal and Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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 - model: saveAPI.gallery
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 10) Sinusoidal Steady state Analysis, 10.9) Superposition Source Transformations
       and Thevenin theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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 - model: saveAPI.gallery
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   fields:
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 12) Polyphase Circuits, 12.1) Single phase three wire systems'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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 - model: saveAPI.gallery
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   fields:
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     name: ex13_7
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 13) Magnetically coupled circuits, 13.7) The Ideal Transformer'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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 - model: saveAPI.gallery
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   fields:
     save_id: gallery51
     name: ex17_4
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 17) Two Port Networks, 17.4) Admittance parameters'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 674
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   fields:
     save_id: gallery52
     name: ex18_2
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 18) Fourier Circuit Analysis, 18.2) Complete Response to periodic Forcing
       Functions'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     media: gallery52.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 675
+  pk: 54
   fields:
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     name: ex18_8
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 18) Fourier Circuit Analysis, 18.8) The physical significance of system
       function'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="ex18_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -81811,14 +103774,15 @@
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     media: gallery53.png
+    script_dump: ''
 - model: saveAPI.gallery
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   fields:
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     name: ex3_11
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.11) Resistors in series and parallel'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_11"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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     media: gallery54.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 56
   fields:
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     name: ex3_13
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.13) Voltage and Current division'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_13"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -83017,14 +104982,15 @@
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     media: gallery55.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 57
   fields:
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     name: ex3_14
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.14) Voltage and Current division'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_14"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -83584,14 +105550,15 @@
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     media: gallery56.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 58
   fields:
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     name: ex3_1
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.1) Kirchoff current law'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_1"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -84218,14 +106185,15 @@
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     media: gallery57.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 59
   fields:
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     name: ex3_2
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.2) Kirchoff voltage law'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -84767,14 +106735,15 @@
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       as="defaultParent" id="-3721b5e:1319cfae9ac:-7f30" parent="-3721b5e:1319cfae9ac:-7f2f"/></XcosDiagram>
     media: gallery58.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 60
   fields:
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     name: ex3_3
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.3) Kirchoff voltage law'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_3"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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       as="defaultParent" id="-16593537:1319d63fbbf:-7f80" parent="-16593537:1319d63fbbf:-7f7f"/></XcosDiagram>
     media: gallery59.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 61
   fields:
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     name: ex3_4
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.4) Kirchoff voltage law'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_4"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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       as="defaultParent" id="-5fcba885:134ccedce1f:-8000" parent="-5fcba885:134ccedce1f:-7fff"/></XcosDiagram>
     media: gallery60.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 683
+  pk: 62
   fields:
     save_id: gallery61
     name: ex3_5
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.5) The Single Loop Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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       as="defaultParent" id="-5fcba885:134ccedce1f:-7cf6" parent="-5fcba885:134ccedce1f:-7cf5"/></XcosDiagram>
     media: gallery61.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 63
   fields:
     save_id: gallery62
     name: ex3_6
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.6) The single node pair circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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     media: gallery62.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 685
+  pk: 64
   fields:
     save_id: gallery63
     name: ex3_9
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 3) Voltage and Current laws, 3.9) Series and Parallel connected sources'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex3_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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     media: gallery63.png
+    script_dump: ''
 - model: saveAPI.gallery
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+  pk: 65
   fields:
     save_id: gallery64
     name: ex4_10
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.10) Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_10"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
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     media: gallery64.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 687
+  pk: 66
   fields:
     save_id: gallery65
     name: ex4_11
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.11) The Supermesh'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_11"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -89797,14 +111772,15 @@
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     media: gallery65.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 688
+  pk: 67
   fields:
     save_id: gallery66
     name: ex4_12
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.12) The Supermesh'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_12"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -91144,14 +113120,15 @@
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       as="defaultParent" id="5e6a3066:134dff9ba34:-7ffe" parent="5e6a3066:134dff9ba34:-7ffd"/></XcosDiagram>
     media: gallery66.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 689
+  pk: 68
   fields:
     save_id: gallery67
     name: ex4_1
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.1) Nodal analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_1"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -91806,14 +113783,15 @@
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       id="-16b82e93:131e810ab25:-8000" parent="-16b82e93:131e810ab25:-7fff"/></XcosDiagram>
     media: gallery67.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 690
+  pk: 69
   fields:
     save_id: gallery68
     name: ex4_2
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.2) Nodal analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -93108,14 +115086,15 @@
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       id="-16b82e93:131e810ab25:-7f1e" parent="-16b82e93:131e810ab25:-7f1d"/></XcosDiagram>
     media: gallery68.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 691
+  pk: 70
   fields:
     save_id: gallery69
     name: ex4_5
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.5) The supernode'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -93949,14 +115928,15 @@
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       id="-5f02711f:131ec3f74c9:-8000" parent="-5f02711f:131ec3f74c9:-7fff"/></XcosDiagram>
     media: gallery69.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 692
+  pk: 71
   fields:
     save_id: gallery70
     name: ex4_6
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.6) The supernode'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -96016,14 +117996,15 @@
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       as="defaultParent" id="5e6a3066:134dff9ba34:-7e89" parent="5e6a3066:134dff9ba34:-7e88"/></XcosDiagram>
     media: gallery70.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 693
+  pk: 72
   fields:
     save_id: gallery71
     name: ex4_7
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.7) Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -96726,14 +118707,15 @@
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       id="-5f02711f:131ec3f74c9:-7da1" parent="-5f02711f:131ec3f74c9:-7da0"/></XcosDiagram>
     media: gallery71.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 694
+  pk: 73
   fields:
     save_id: gallery72
     name: ex4_8
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.8) Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -97807,14 +119789,15 @@
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       id="-5f02711f:131ec3f74c9:-7c8d" parent="-5f02711f:131ec3f74c9:-7c8c"/></XcosDiagram>
     media: gallery72.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 695
+  pk: 74
   fields:
     save_id: gallery73
     name: ex4_9
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 4) Basic Nodal and Mesh Analysis, 4.9) Mesh analysis'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex4_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -98467,15 +120450,16 @@
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       id="-5f02711f:131ec3f74c9:-7e53" parent="-5f02711f:131ec3f74c9:-7e52"/></XcosDiagram>
     media: gallery73.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 696
+  pk: 75
   fields:
     save_id: gallery74
     name: ex6_11
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.11) Thevenin
       and Norton Equivalent circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex6_11"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -98977,15 +120961,16 @@
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       as="defaultParent" id="2602728:132d47c9ecc:-8000" parent="2602728:132d47c9ecc:-7fff"/></XcosDiagram>
     media: gallery74.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 697
+  pk: 76
   fields:
     save_id: gallery75
     name: ex6_13
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.13) Thevenin
       and Norton Equivalent circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex6_13"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -99749,15 +121734,16 @@
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       as="defaultParent" id="2602728:132d47c9ecc:-7f5b" parent="2602728:132d47c9ecc:-7f5a"/></XcosDiagram>
     media: gallery75.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 698
+  pk: 77
   fields:
     save_id: gallery76
     name: ex6_14
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.14) Thevenin
       and Norton Equivalent circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex6_14"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -100771,15 +122757,16 @@
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       as="defaultParent" id="-1f470ada:134d070a228:-7f33" parent="-1f470ada:134d070a228:-7f32"/></XcosDiagram>
     media: gallery76.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 699
+  pk: 78
   fields:
     save_id: gallery77
     name: ex6_15
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.15) Thevenin
       and Norton Equivalent circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.16) Maximum
       power transfer'
-    save_time: 2025-01-23 16:04:57+00:00
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     book: 215
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       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     name: ex6_20
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.20) Compensation
       Theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.21) Compensation
       Theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     name: ex6_23
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.23) Source
       Transformations'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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       Transformations'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.3) The
       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 6) Network Theorems and useful Circuit Analysis Techniques, 6.6) The
       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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       Superposition principle'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
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   fields:
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     name: ex7_11
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 7) Capacitors and Inductors, 7.11) Modeling Capacitors and Inductors'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 8) Basic RL and RC circuits, 8.10) Driven RC circuits'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     media: gallery90.png
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 8) Basic RL and RC circuits, 8.1) The Source free RL Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 8) Basic RL and RC circuits, 8.2) The Source free RL Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 8) Basic RL and RC circuits, 8.3) The Source free RC Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 8) Basic RL and RC circuits, 8.4) A more General Perspective'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
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-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     name: ex9_2
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.2) The Overdamped parallel circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
 - model: saveAPI.gallery
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.3) The Overdamped parallel circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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+    script_dump: ''
 - model: saveAPI.gallery
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   fields:
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     name: ex9_6
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.6) The Underdamped parallel RLC circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.7) The Source free series RLC Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
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   fields:
     save_id: gallery101
     name: ex9_8
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.8) The Source free series RLC Circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="ex9_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -119611,14 +141622,15 @@
       x="500.0" y="70.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="1f781c6f:13506286c0b:-7ffe" parent="1f781c6f:13506286c0b:-7ffd"/></XcosDiagram>
     media: gallery101.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 724
+  pk: 103
   fields:
     save_id: gallery102
     name: ex9_9
     description: 'Engineering Circuit Analysis (Author: W. Hayt, J. Kemmerly And S.
       Durbin), 9) The RLC Circuit, 9.9) The Complete response of RLC circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 215
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="ex9_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -120272,14 +142284,15 @@
       x="600.0" y="180.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="1f781c6f:13506286c0b:-7d57" parent="1f781c6f:13506286c0b:-7d56"/></XcosDiagram>
     media: gallery102.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 725
+  pk: 104
   fields:
     save_id: gallery103
     name: Ex6_23
     description: 'Electrical Machines (Author: R. K. Srivastava), 6) Synchronous Machines,
       6.23) To find maximum value of power angle and maximum value of overshoot'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 2777
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       title="Ex6_23"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406 2040--><Array as="context"
@@ -120795,14 +142808,116 @@
       as="geometry" height="40.0" width="40.0" x="440.0" y="310.0"/></BasicBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="6521d368:1479034e794:-7fa0" parent="6521d368:1479034e794:-7f9f"/></XcosDiagram>
     media: gallery103.png
+    script_dump: '
+
+      // ELECTRICAL MACHINES
+
+      // R.K.Srivastava
+
+      // First Impression 2011
+
+      // CENGAGE LEARNING INDIA PVT. LTD
+
+      // CHAPTER : 6 : SYNCHRONOUS MACHINES
+
+
+      // EXAMPLE : 6.23
+
+
+      // GIVEN DATA
+
+
+      p = 4;                          // Number of the poles in the Alternator
+
+      f = 50;                         // Frequency in Hertz
+
+      pkw = 500;                      // Alternator delivering load in kilo-watts
+
+      pkwinc = 1000;                  // Generator increases its share of the common
+      elictrical in kilo-watts
+
+      Kj = 1.5;                       // Inertia acceleration coefficient for the
+      combined prime mover-alternator in N-m/elec deg/second square
+
+      Kd = 12;                        // Damping torque coefficient in N-m/elec deg/second
+
+      delta1 = 9;                     // Initial value of the Power angle in degree
+
+
+
+      // CALCULATIONS
+
+
+      delta2 = (pkwinc/pkw)*delta1;                               // Final value (maximum
+      value) of the Power angle in degree (considering Linear variation)
+
+      ws = (4*%pi*f)/p;                                           // Rotational speed
+      in Radians per second
+
+      Ts = (pkw*1000)/ws;                                         // Synchornizing
+      torque at 500kW in N-m
+
+      Ks = Ts/delta1;                                             // Synchornizing
+      torque cofficient at 500kW in N-m/elec-deg
+
+      // Laplace transform of the swing Equation can be written as :- s^2 + ((Kd/Kj)*s)
+      + (Ks/Kj) = 0, s^2 + (12/1.5)s + (353.86/1.5) = 0 and compring with the standard
+      equation s^2 + s(2*zeta*Wn) + Wn^2 = 0 we get:- mentined below  (refer page
+      no. 454 and 455)
+
+      Wn = sqrt(Ks/Kj);                                           // Natural frequency
+      of oscillations in Radians per second
+
+      fn = Wn/(2*%pi);                                            // Frequency of
+      natural oscillations in Hertz
+
+      zeta = (1*Kd)/(2*Wn*Kj);                                    // Damping ratio
+
+      Wd = Wn*(sqrt(1-zeta^2));                                   // Frequency of
+      damped oscillations in radians/s
+
+      fd = Wd/(2*%pi);                                            // Frequency of
+      damped oscillations in Hertz
+
+      ts = 5/(zeta*Wn);                                           // Settling time
+      in second
+
+      deltamax = delta1 + 1.42*(delta2-delta1);                   // The maximum overshoot
+      for damping ratio of 0.2604 is about 42% the maximum appoximate value of the
+      overshoot in terms of 1% tolearance band in Electrical degree
+
+
+
+      // DISPLAY RESULTS
+
+
+      disp("EXAMPLE : 6.23: SOLUTION :-");
+
+      printf("\n (a.1) Final value (maximum value) of the Power angle (considering
+      Linear variation), delta2 = %.f degree \n",delta2)
+
+      printf("\n (a.2) Natural frequency of oscillations, Ns = %.2f radians/s \n",Wn)
+
+      printf("\n (a.3) Damping ratio, zeta = %.4f \n",zeta)
+
+      printf("\n (a.4) Frequency of damped oscillations, Wd = %.2f radians/s \n",Wd)
+
+      printf("\n (a.5) Settling time, ts = %.2f seconds \n",ts)
+
+      printf("\n  (b)  The maximum overshoot for damping ratio of 0.2604 is about
+      42 percent the maximum appoximate value of the overshoot in terms of 1 percent
+      tolearance band is, deltamax = %.2f degree \n",deltamax)
+
+      printf("\n\n FOR CASE (C) CANNOT BE DO IT IN THIS BECAUSE AS IT REQUIRES MATLAB
+      SIMULINK \n")'
 - model: saveAPI.gallery
-  pk: 726
+  pk: 105
   fields:
     save_id: gallery104
     name: eg12_2
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 12) Simplifying
-      logical functions, 12.2) Prove the given theorem'
-    save_time: 2025-01-23 16:04:57+00:00
+      logical functions, 12.2) Prove the given theoram'
+    save_time: 2025-03-17 15:49:08+00:00
     book: 293
     data_dump: '<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="4.0" title="eg12_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -122869,15 +144984,16 @@
       id="47283b12:1341c9b3c8b:-78f7" parent="47283b12:1341c9b3c8b:-78f6"/><mxPoint
       as="origin" x="-10.0"/></XcosDiagram>'
     media: gallery104.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 727
+  pk: 106
   fields:
     save_id: gallery105
     name: eg12_3a
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 12) Simplifying
       logical functions, 12.3.a) Design a digital logic circuit that provides logic
       1 whenever majority votes yes'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="8.0" title="eg12_3a"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -125999,14 +148115,15 @@
       as="geometry" height="40.0" width="40.0" x="520.0" y="200.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="47283b12:1341c9b3c8b:-8000" parent="47283b12:1341c9b3c8b:-7fff"/></XcosDiagram>
     media: gallery105.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 728
+  pk: 107
   fields:
     save_id: gallery106
     name: eg12_3b
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 12) Simplifying
       logical functions, 12.3.b) Modify part A so that only NAND gates are used'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:08+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="8.0" title="eg12_3b"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -129126,14 +151243,15 @@
       height="40.0" width="40.0" x="50.0" y="330.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="47283b12:1341c9b3c8b:-7c5b" parent="47283b12:1341c9b3c8b:-7c5a"/></XcosDiagram>
     media: gallery106.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 729
+  pk: 108
   fields:
     save_id: gallery107
     name: eg2_10
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 2) The
       circuit elements, 2.10) Design an opamp circuit solution of the given equation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg2_10"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -131666,14 +153784,15 @@
       x="190.0" y="180.0"/><mxPoint as="targetPoint" x="310.0" y="180.0"/></mxGeometry></ImplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="200893ff:13428736452:-8000" parent="200893ff:13428736452:-7fff"/></XcosDiagram>
     media: gallery107.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 730
+  pk: 109
   fields:
     save_id: gallery108
     name: eg3_10
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.10) Find the value of the node pair voltages V1 and V2'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_10"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -132519,14 +154638,15 @@
       height="40.0" width="40.0" x="490.0" y="180.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-7b1d" parent="-108078b6:1345b8f2778:-7b1c"/></XcosDiagram>
     media: gallery108.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 731
+  pk: 110
   fields:
     save_id: gallery109
     name: eg3_11
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.11) Find the branch current flowing through R2'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: '<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_11"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -133145,14 +155265,15 @@
       height="40.0" width="40.0" x="110.0" y="430.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-79f9" parent="-108078b6:1345b8f2778:-79f8"/></XcosDiagram>'
     media: gallery109.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 732
+  pk: 111
   fields:
     save_id: gallery110
     name: eg3_14
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.14) Find the value of the output voltage'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_14"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -133758,14 +155879,15 @@
       x="460.0" y="190.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-794d" parent="-108078b6:1345b8f2778:-794c"/></XcosDiagram>
     media: gallery110.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 733
+  pk: 112
   fields:
     save_id: gallery111
     name: eg3_15
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.15) Find the current delivered to the source by the network'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_15"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -134438,14 +156560,15 @@
       as="geometry" height="40.0" width="40.0" x="270.0" y="280.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-78b9" parent="-108078b6:1345b8f2778:-78b8"/></XcosDiagram>
     media: gallery111.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 734
+  pk: 113
   fields:
     save_id: gallery112
     name: eg3_5
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.5) Determine the current which flows through R2'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -135092,14 +157215,15 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="40.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-8000" parent="-108078b6:1345b8f2778:-7fff"/></XcosDiagram>
     media: gallery112.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 735
+  pk: 114
   fields:
     save_id: gallery113
     name: eg3_6
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.6) Find the power dissipation in R1'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -135832,14 +157956,15 @@
       as="geometry" height="40.0" width="40.0" x="560.0" y="70.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-7edc" parent="-108078b6:1345b8f2778:-7edb"/></XcosDiagram>
     media: gallery113.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 736
+  pk: 115
   fields:
     save_id: gallery114
     name: eg3_7
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.7) Find the current which flows through R2'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -136766,15 +158891,16 @@
       width="40.0" x="380.0" y="280.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-7e22" parent="-108078b6:1345b8f2778:-7e21"/></XcosDiagram>
     media: gallery114.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 737
+  pk: 116
   fields:
     save_id: gallery115
     name: eg3_9
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 3) Elementary
       network theory, 3.9) Find the magnitude and direction of each of the branch
       currents'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="eg3_9"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -137492,15 +159618,16 @@
       as="geometry" height="40.0" width="40.0" x="200.0" y="380.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-108078b6:1345b8f2778:-7bff" parent="-108078b6:1345b8f2778:-7bfe"/></XcosDiagram>
     media: gallery115.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 738
+  pk: 117
   fields:
     save_id: gallery116
     name: eg5_1
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.1) Find the expression for the current flowing
       through the circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="eg5_1"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -138352,15 +160479,16 @@
       x="120.0" y="20.0"/></TextBlock></root></mxGraphModel><mxCell as="defaultParent"
       id="7ce57742:133f8596f12:-7f12" parent="7ce57742:133f8596f12:-7f11"/></XcosDiagram>
     media: gallery116.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 739
+  pk: 118
   fields:
     save_id: gallery117
     name: eg5_2
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.2) Find the expression for the current flowing
       through the circuit and the total energy dissipated in the resistor'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="eg5_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -139101,15 +161229,32 @@
       x="344.0" y="140.0"/><mxPoint as="targetPoint" x="420.0" y="140.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="4c3b265:134192dde3e:-7ed0" parent="4c3b265:134192dde3e:-7ecf"/></XcosDiagram>
     media: gallery117.png
+    script_dump: 'C = 10*10^-6 ; //capacitance(in farads)
+
+      R = 0.2*10^6; //resistance (in ohms)
+
+      Vi = 40; //initial voltage of the capacitor (in volts)
+
+      Wc = (1/2)*C*Vi^2; //energy stored in the capacitor
+
+      //current flowing in circuit as a function of time i(t) = 2*10^-4*exp(-t/2)
+
+      //power dissipated in the resistor = R*i^2
+
+      Wr = integrate(''R*4*10^-8*exp(-t)'',''t'',0,100)
+
+      disp(Wc,"energy stored in the capacitor(in Joules) = ")
+
+      disp(Wr,"energy dissipated in the resistor(in Joules) = ")'
 - model: saveAPI.gallery
-  pk: 740
+  pk: 119
   fields:
     save_id: gallery118
     name: eg5_3
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.3) Determine the voltage which appears across
       each capacitor at steady state'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="50.0" title="eg5_3"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -140006,15 +162151,16 @@
       height="40.0" width="40.0" x="260.0" y="390.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="4c3b265:134192dde3e:-7e2e" parent="4c3b265:134192dde3e:-7e2d"/></XcosDiagram>
     media: gallery118.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 741
+  pk: 120
   fields:
     save_id: gallery119
     name: eg5_5
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.5) Find the complete solution for the charge
       on the capacitor and show a plot of the response'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="eg5_5"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -140927,15 +163073,16 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitInputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="4c3b265:134192dde3e:-7d26" parent="4c3b265:134192dde3e:-7d25"/></XcosDiagram>
     media: gallery119.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 742
+  pk: 121
   fields:
     save_id: gallery120
     name: eg5_6
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.6) Describe the dynamic behaviour of the given
       circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="eg5_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -141790,15 +163937,16 @@
       width="40.0" x="230.0" y="360.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="4c3b265:134192dde3e:-7bc3" parent="4c3b265:134192dde3e:-7bc2"/></XcosDiagram>
     media: gallery120.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 743
+  pk: 122
   fields:
     save_id: gallery121
     name: eg5_7
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.7) Obtain the critically damped response for
       the circuit'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="eg5_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -142650,15 +164798,16 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="40.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="774ef901:13456c50b60:-7ee1" parent="774ef901:13456c50b60:-7ee0"/></XcosDiagram>
     media: gallery121.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 744
+  pk: 123
   fields:
     save_id: gallery122
     name: eg5_8
     description: 'Electrical Engineering Fundamentals (Author: V. Del Toro), 5) Circuit
       dynamics and forced responses, 5.8) Repeat the previous example for the case
       where the resistance R is changed'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 293
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="eg5_8"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -143511,15 +165660,16 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="40.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="774ef901:13456c50b60:-7e9f" parent="774ef901:13456c50b60:-7e9e"/></XcosDiagram>
     media: gallery122.png
+    script_dump: ''
 - model: saveAPI.gallery
-  pk: 745
+  pk: 124
   fields:
     save_id: gallery123
     name: Ex6_14_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 6) The Frequency Response Design Method, 6.14)
       Lead compensation for DC motor'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex6_14_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -144742,15 +166892,28 @@
       y="120.0"/></Array></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery123.png
+    script_dump: '//Example 6.14
+
+      //Lead compensation for DC motor.
+
+
+      // the required value
+
+      // for step response, set sw to 2
+
+      // for ramp response, set sw to 0
+
+
+      sw=2'
 - model: saveAPI.gallery
-  pk: 746
+  pk: 125
   fields:
     save_id: gallery124
     name: Ex7_32_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 7) State Space Design, 7.32) Redesign of the
       Dc servo compensator using SRL'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex7_32_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -145972,15 +168135,198 @@
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><mxPoint
       as="origin" y="-2.0"/></XcosDiagram>
     media: gallery124.png
+    script_dump: '//------------------------------------------------------------------
+
+      //------------------------------------------------------------------
+
+      //A function written by Deepti Khimani.
+
+      //Usage:-
+
+      //p=zpk_dk(sl)
+
+      //[p, z]=zpk_dk(sl)
+
+      //[p, z, k]=zpk_dk(sl)
+
+      //p:- Poles of the system
+
+      //z:- zeros of the system
+
+      //k:- DC gain of the system
+
+      //------------------------------------------------------------------
+
+      //------------------------------------------------------------------
+
+
+      function[pl,zr,k]=zpk_dk(sysmodel)
+
+      [lhs,rhs]=argn(0)
+
+
+      if rhs == 0 then
+
+      disp(["p=zpk_dk(sl)";"[p, z]=zpk_dk(sl)";"[p, z, k]=zpk_dk(sl)"]);
+
+      disp(["p:- Poles of the system";"z:- zeros of the system"]);
+
+      disp("k:- DC gain of the system");
+
+      return;
+
+      end
+
+
+      if typeof(sysmodel)=="rational" then
+
+      sys=tf2ss(sysmodel);
+
+      pl=spec(sys.A);
+
+      zr=trzeros(sys);
+
+      temp1=poly(zr,''s'',''roots'')/poly(pl,''s'',''roots'');
+
+      temp2=sysmodel/temp1;
+
+      temp3=tf2ss(temp2);
+
+      k=temp3.D;
+
+      elseif typeof(sysmodel)=="state-space" then
+
+      pl=spec(sysmodel.A);
+
+      zr=trzeros(sysmodel);
+
+      g=ss2tf(sysmodel);
+
+      temp1=poly(zr,''s'',''roots'')/poly(pl,''s'',''roots'');
+
+      temp2=g/temp1;
+
+      temp3=tf2ss(temp2);
+
+      k=temp3.D
+
+      else
+
+      error("Wrong type of input argument.")
+
+      end
+
+      endfunction
+
+
+      //Example 7.32
+
+      // Redesign of the Dc servo compensator using SRL
+
+
+      // State space representation
+
+      //Transfer function model for DC Servo
+
+      s=poly(0,''s'');
+
+      num=10;
+
+      den=s*(s+2)*(s+8);
+
+      Gs=syslin(''c'',num/den);
+
+
+      // State space representation
+
+      F=[-10 1 0;-16 0 1;0 0 0]
+
+      G=[0 0 10]'';
+
+      H=[1 0 0];
+
+      J=0;
+
+      n=sqrt(length(F));
+
+      //Desired poles for the DC Servo system.
+
+      Pc=[-2+1.56*%i -2-1.56*%i -8.04]
+
+
+
+      // State feedback gain
+
+      K=ppol(F,G,Pc)
+
+      disp(K,''K='',"State feedback gain")
+
+
+      //Estimator - error roots are at
+
+      Pe=[-4+4.49*%i -4-4.49*%i -9.169]
+
+      Lt=ppol(F'',H'',Pe);
+
+      L=clean(Lt'');
+
+      disp(L,''L='',"Observer gain")
+
+      //Error in book, Gain values are different in book.
+
+      //------------------------------------------------------------------
+
+      //Compensator Design
+
+      DK=-K*inv(s*eye(n,n)-F+G*K+L*H)*L;
+
+      DK=syslin(''c'',DK)
+
+      [pl,zr,Kp]=zpk_dk(DK);
+
+      Dc=poly(zr,''s'',''roots'')/poly(pl,''s'',''roots'')
+
+      //------------------------------------------------------------------
+
+      //symmetric root locus
+
+      G_s=horner(Gs,-s);
+
+      evans(Gs*G_s)
+
+      //root locus
+
+      evans(Gs*Dc) //Correct root locus
+
+      //Discrete-time controller
+
+      nc=94.5*conv([7.98 1],[2.52 1])
+
+      dc=conv([59.5348 8.56 1],[10.6 1])
+
+      sysDc=poly(nc,''s'',''coeff'')/poly(dc,''s'',''coeff'');
+
+      sysDc_ss=syslin(''c'',tf2ss(sysDc));
+
+      ts=0.1;
+
+      sysDd=dscr(sysDc_ss,ts)
+
+      Gdz=ss2tf(sysDd);
+
+
+      disp(sysDc,"Continuous-time compensator")
+
+      disp(Gdz,"Discrete-time compensator")'
 - model: saveAPI.gallery
-  pk: 747
+  pk: 126
   fields:
     save_id: gallery125
     name: Ex7_34_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 7) State Space Design, 7.34) Servomechanism
       increasing the velocity constant through zero assignment'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex7_34_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -147464,15 +169810,238 @@
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><mxPoint
       as="origin" y="-12.0"/></XcosDiagram>
     media: gallery125.png
+    script_dump: '//Example 7.34
+
+      // Servomechanism, increasing the velocity constant through
+
+      // zero assignment.
+
+
+      // State space representation
+
+      //Transfer function model for DC Servo
+
+      s=poly(0,''s'');
+
+      num=1;
+
+      den=s*(s+1);
+
+      Gs=syslin(''c'',num/den);
+
+
+      // State space representation
+
+      F=[0 1;0 -1]
+
+      G=[0 1]'';
+
+      H=[1 0];
+
+      J=0;
+
+      n=sqrt(length(F));
+
+      //Desired poles for the DC Servo system.
+
+      Pc=[-2 -2]
+
+
+      // State feedback gain
+
+      //------------------------------------------------------------------
+
+      //------------------------------------------------------------------
+
+      //A function written by Deepti Khimani.
+
+      //Usage:-
+
+      //[K, lambda]=acker_dk(a, b, pl)
+
+      //K=acker_dk(a, b, pl)
+
+      //a:- System matrix.
+
+      //b:- input matrix.
+
+      //p:- Desired poles.
+
+      //K:-State feedback gain for the control law u=-Kx.
+
+      //lambda:- Eigen values of (a-b*k)
+
+      //------------------------------------------------------------------
+
+      //------------------------------------------------------------------
+
+
+      function [K, lambda]=acker_dk(a, b, pl)
+
+      [lhs,rhs]=argn(0)
+
+
+      if rhs == 0 then
+
+      disp(["K=acker_dk(a, b, pl)";"[K, lambda]=acker_dk(a, b, pl)"]);
+
+      disp(["a:- System matrix";"b:- input matrix";"p:- Desired poles"]);
+
+      disp(["K:-State feedback gain for the control law u=-Kx";...
+
+      "lambda:- Eigen values of (a-b*k)"]);
+
+      return;
+
+      end
+
+      [ra ca]=size(a);
+
+      [rb cb]=size(b);
+
+      l=length(pl);
+
+
+      CO=cont_mat(a,b);
+
+
+      if ra~=l then
+
+      error(["Dimension error:";"number of desired poles must equal...
+
+      to order of the system"]);
+
+      elseif ra~=ca then
+
+      error(["Dimension error:";"system matrix should be...
+
+      a sqaure matrix"]);
+
+      elseif rb~=ra then
+
+      error (["Dimension error:","Input matrix should have...
+
+      as many rows as a system matrix."]);
+
+      elseif rank(CO)<ra then
+
+      error("system is not controllable");
+
+      end
+
+      //------------------------------------------------------------------
+
+      //controllable canonical form
+
+      [Ac,Bc,T,ind]=canon(a,b);
+
+
+      //CO=zeros(ra,cb);
+
+      for i=1:ra
+
+      CO(:,ra+1-i)=Ac^(i-1)*Bc;
+
+      end
+
+      //------------------------------------------------------------------
+
+      chr_eq=poly(pl,''s'');
+
+      des_chr_coeff=coeff(chr_eq);
+
+
+      des_chr_coeff=des_chr_coeff(1:ra);
+
+      alpha_c=Ac^ra;
+
+
+      for k=1:ra
+
+      alpha_c=alpha_c + des_chr_coeff(k)*Ac^(k-1)
+
+      end
+
+      //------------------------------------------------------------------
+
+      //State feedback gain
+
+      temp=zeros(1,ra);
+
+      temp(1)=1;
+
+      K=temp*inv(CO)*alpha_c;
+
+      K=K/T;
+
+      lambda=spec(a-b*K);
+
+      endfunction
+
+      //------------------------------------------------------------------
+
+      K=acker_dk(F,G,Pc)//Gain computed in book is incorrect.
+
+      disp(K,''K='',"State feedback gain")
+
+      //------------------------------------------------------------------
+
+      //Overall transfer function with reduced order estimator.
+
+      Gred=8.32*(0.096+s)/(0.1 +s)/(8 + 4*s+s^2)
+
+      Gred=syslin(''c'',Gred)
+
+      disp(Gred,''Ys/Rs'',"Overall transfer function with reduced...
+
+      order estimator")
+
+
+      //Compensator
+
+      D=(0.096+s)*(s+1)/(4.08 +s)/(0.0196+s)
+
+      Ds=syslin(''c'',D*8.32)
+
+      disp(Ds,''Ds='',"Compensator transfer function")
+
+      //------------------------------------------------------------------
+
+      //root locus
+
+      evans(D*Gs,100) //Correct root locus
+
+      //------------------------------------------------------------------
+
+      //step response of the system with lag compensation
+
+      t=0:0.1:5;
+
+      ylag=csim(''step'',t,8.32*Gs*D/(1+8.32*Gs*D));
+
+      //------------------------------------------------------------------
+
+      //Discrete-time controller
+
+      sysDc_ss=syslin(''c'',tf2ss(Ds));
+
+      ts=0.1;
+
+      sysDd=dscr(sysDc_ss,ts)
+
+      Gdz=ss2tf(sysDd)
+
+
+      disp(Gdz,"Discrete-time compensator")'
 - model: saveAPI.gallery
-  pk: 748
+  pk: 127
   fields:
     save_id: gallery126
     name: Ex7_35_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 7) State Space Design, 7.35) Integral Control
       of a Motor Speed System'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex7_35_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -149302,15 +171871,74 @@
       x="940.0" y="260.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery126.png
+    script_dump: '//Example 7.35
+
+      // Integral Control of a Motor Speed System
+
+
+      //Transfer function model
+
+      num=1;
+
+      s=poly(0,''s'');
+
+      den=(s+3);
+
+      G=syslin(''c'',num/den);
+
+      sys=tf2ss(G)
+
+
+      // State space representation of augmented system
+
+      F=[0 1; 0 -3];
+
+      G=[0 1]'';
+
+      H=[1 0];
+
+      J=0;
+
+
+      //Desired poles for augmented system
+
+      Pc=[-5 -5];
+
+
+      // State feedback gain is
+
+      K=ppol(F,G,Pc)
+
+
+      //Estimator
+
+      Pe=[-10];
+
+      L=ppol(sys.A'',sys.C'',Pe)
+
+
+      // (c) Compare step reference and disturbance response.
+
+
+      // the required values
+
+      // for step reference response switch, set r to 1 and w to 0
+
+      // for step disturbance response switch, set r to 0 and w to 1
+
+
+      r=1
+
+      w=0'
 - model: saveAPI.gallery
-  pk: 749
+  pk: 128
   fields:
     save_id: gallery127
     name: Ex8_1_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 8) Digital Control, 8.1) Digital Controller
       using tustin approximation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="2.0" title="Ex8_1_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -150525,15 +173153,53 @@
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/><mxPoint
       as="origin" y="-3.0"/></XcosDiagram>
     media: gallery127.png
+    script_dump: '///Example 8.1
+
+      // Digital Controller using tustin approximation.
+
+
+      //Cntroller
+
+      s=poly(0,''s'');
+
+      numD=s/2+1;
+
+      denD=s/10+1;
+
+      D=10*numD/denD;
+
+      Ds=syslin(''c'',D);
+
+      //sampling freq. = 25 times bandwidth
+
+      Wbw=10;
+
+      Ws=25*Wbw;
+
+      fs=Ws/2/%pi;
+
+      T=1/fs; //sampling time
+
+      a=1;b=-1;
+
+      c=1;d=1;
+
+      //Digital controller
+
+      z=poly(0,''z'');
+
+      Dz=horner(Ds,2/T*(a*z+b)/(c*z+d));
+
+      disp(Dz,''Digital Controller : '')'
 - model: saveAPI.gallery
-  pk: 750
+  pk: 129
   fields:
     save_id: gallery128
     name: Ex8_2_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 8) Digital Control, 8.2) Design of a Space Station
       Attitude Digital Controller using Discrete Equivalents'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex8_2_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -152228,15 +174894,73 @@
       scilabClass=""><mxPoint x="810.0" y="160.0"/><mxPoint x="810.0" y="110.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery128.png
+    script_dump: '//Example 8.2
+
+      // Design of a Space Station Attitude Digital Controller using
+
+      // Discrete Equivalents
+
+
+      // State space representation of continuous time system
+
+      s=poly(0,''s'');
+
+      num=1;
+
+      den=(s^2);
+
+      Gs=syslin(''c'',num/den);
+
+      Ds=0.81*(s+0.2)/(s+2);
+
+      Ds=syslin(''c'',Ds);
+
+      sysc=Gs*Ds;
+
+
+      //Root locus
+
+      evans(sysc)
+
+      //Contonuous time response of the system
+
+      tc=0:0.1:30;
+
+      syscl=sysc/(1+sysc)
+
+      yc=csim("step",tc,syscl);
+
+      //------------------------------------------------------------------
+
+      // Discretization of the system at
+
+      z=poly(0,''z'')
+
+      // sampling time Ts=1 sec
+
+      Ts=1;
+
+      Dz1=horner(Ds,2/Ts*(z-1)/(z+1))
+
+      disp(Dz1,"Dz1=","Discrete-time controller with Ts=1 sec.")
+
+
+      // sampling time Ts=0.5 sec
+
+      Ts2=0.5;
+
+      Dz2=horner(Ds,2/Ts2*(z-1)/(z+1))
+
+      disp(Dz2,"Dz2=","Discrete-time controller with Ts=0.5 sec.")'
 - model: saveAPI.gallery
-  pk: 751
+  pk: 130
   fields:
     save_id: gallery129
     name: Ex9_11_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.11) Describing Function
       for a relay with hysteresis non linearity'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex9_11_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -152800,15 +175524,61 @@
       x="370.0" y="120.0"/><mxPoint as="targetPoint" x="370.0" y="170.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery129.png
+    script_dump: '//Example 9.11
+
+      //Describing Function for a relay with hysteresis nonlinearity.
+
+
+      //Response of the saturation noninearity to sinusoidal input
+
+      ////Describing Functin for relay with hysteresis nonlinearity.
+
+      h=0.1;
+
+      N=1;
+
+      i=1;
+
+
+      for a=0.1:0.025:1
+
+      if a<h then
+
+      Keq(i,1)=0;
+
+      ro(i,1)=0;
+
+      theta(i,1)=0;
+
+      else
+
+      Keq(i,1)=4*N/(%pi*a)*(sqrt(1-(h/a)^2)-%i*h/a);
+
+      [r th]=polar(Keq(i,1));
+
+      ro(i,1)=r; //magnitude
+
+      theta(i,1)=clean(th); //angle in radians
+
+      end
+
+      i=i+1;
+
+      end
+
+
+      a=0.1:0.025:1;
+
+      a=a'';'
 - model: saveAPI.gallery
-  pk: 752
+  pk: 131
   fields:
     save_id: gallery130
     name: Ex9_13_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.13) Determination of
       stability with a hysteresis nonlinearity'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="50.0" title="Ex9_13_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -153388,15 +176158,60 @@
       x="590.0" y="170.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery130.png
+    script_dump: '//Example 9.13
+
+      //Determination of stability with a hysteresis nonlinearity.
+
+
+      //System Model
+
+      s=poly(0,''s'');
+
+      num=1;
+
+      den=(s^2+s);
+
+      Gs=syslin(''c'',num/den);
+
+
+      // Nyquist Plot of Describing Function for hysteresis nonlinearity
+
+      N=1;
+
+      h=0.1;
+
+      i=1;
+
+
+      for omegat=0:0.05:%pi-0.1;
+
+      a=sin(omegat);
+
+      DF_nyq(i,1)=-%pi/4/N*(sqrt(a^2-h^2) + h * %i);
+
+      i=i+1;
+
+      end
+
+
+      //Response of the system
+
+      K=2;
+
+
+      // the required value
+
+
+      r=1'
 - model: saveAPI.gallery
-  pk: 753
+  pk: 132
   fields:
     save_id: gallery131
     name: Ex9_5_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.5) Changing Overshoot
       and Saturation nonlinearity'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex9_5_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -154061,15 +176876,43 @@
       as="geometry" height="40.0" width="40.0" x="510.0" y="140.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery131.png
+    script_dump: '//Example 9.5
+
+      //Changing Overshoot and Saturation nonlinearity.
+
+
+      //System transfer function and its root locus
+
+
+      s=poly(0,''s'');
+
+      num=(s+1)
+
+      den=(s^2);
+
+      Gs=syslin(''c'',num/den)
+
+
+      //Root locus
+
+      evans(Gs,5)
+
+      // Step response
+
+      K=1;
+
+      i=[2 4 6 8 10 12];
+
+      r=2'
 - model: saveAPI.gallery
-  pk: 754
+  pk: 133
   fields:
     save_id: gallery132
     name: Ex9_6_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.6) Stability of conditionally
       stable system using root locus'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="20.0" title="Ex9_6_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -154674,15 +177517,41 @@
       x="530.0" y="180.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery132.png
+    script_dump: '//Example 9.6
+
+      //Stability of conditionally stable system using root locus.
+
+      //System transfer function and its root locus
+
+
+      s=poly(0,''s'');
+
+      num=(s+1)^2
+
+      den=(s^3);
+
+      Gs=syslin(''c'',num/den)
+
+      //Root locus
+
+      evans(Gs,7)
+
+      //Response of the system
+
+      K=2;
+
+      i=[1 2 3 3.475];
+
+      r=1'
 - model: saveAPI.gallery
-  pk: 755
+  pk: 134
   fields:
     save_id: gallery133
     name: Ex9_7_model_notch
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.7) Analysis and design
       of the system with limit cycle using the root locus'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: '<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="50.0" title="Ex9_7_model_notch"><!--Xcos - 1.0 - scilab-5.5.2
@@ -155354,15 +178223,60 @@
       x="740.0" y="170.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>'
     media: gallery133.png
+    script_dump: '//Example 9.7
+
+      //Analysis and design of the system with limit cycle using the root locus.
+
+      //System transfer function and its root locus
+
+
+      s=poly(0,''s'');
+
+      num=0.1;
+
+      den=(s^2+0.2*s+1)*(s);
+
+      Gs=syslin(''c'',num/den);
+
+
+      //Root locus
+
+      evans(Gs,40)
+
+      //Response of the system
+
+      K=0.5;
+
+      i=[1 4 8];
+
+      r=1
+
+
+      //System with notch compensation
+
+      D=123*(s^2+0.18*s+0.81)/(s+10)^2;
+
+
+      //Root locus
+
+      evans(Gs*D,40)
+
+      //Response of the system witth notch filter
+
+      K=0.5;
+
+      i=[2 4];
+
+      r=2'
 - model: saveAPI.gallery
-  pk: 756
+  pk: 135
   fields:
     save_id: gallery134
     name: Ex9_7_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.7) Analysis and design
       of the system with limit cycle using the root locus'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: '<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="150.0" title="Ex9_7_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -155986,15 +178900,60 @@
       x="750.0" y="170.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>'
     media: gallery134.png
+    script_dump: '//Example 9.7
+
+      //Analysis and design of the system with limit cycle using the root locus.
+
+      //System transfer function and its root locus
+
+
+      s=poly(0,''s'');
+
+      num=0.1;
+
+      den=(s^2+0.2*s+1)*(s);
+
+      Gs=syslin(''c'',num/den);
+
+
+      //Root locus
+
+      evans(Gs,40)
+
+      //Response of the system
+
+      K=0.5;
+
+      i=[1 4 8];
+
+      r=1
+
+
+      //System with notch compensation
+
+      D=123*(s^2+0.18*s+0.81)/(s+10)^2;
+
+
+      //Root locus
+
+      evans(Gs*D,40)
+
+      //Response of the system witth notch filter
+
+      K=0.5;
+
+      i=[2 4];
+
+      r=2'
 - model: saveAPI.gallery
-  pk: 757
+  pk: 136
   fields:
     save_id: gallery135
     name: Ex9_8_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.8) Antiwindup compensation
       for a PI controller'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="10.0" title="Ex9_8_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -157050,15 +180009,38 @@
       x="890.0" y="100.0"/><Array as="points" scilabClass=""><mxPoint x="810.0" y="100.0"/></Array></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery135.png
+    script_dump: '//Example 9.8
+
+      //Antiwindup compensation for a PI controller.
+
+
+      //System Model
+
+
+      //Response of the system
+
+      kp=2;
+
+      ki=4;
+
+
+      //Without antiwindup
+
+      ka=0;
+
+
+      //With antiwindup
+
+      ka=10;'
 - model: saveAPI.gallery
-  pk: 758
+  pk: 137
   fields:
     save_id: gallery136
     name: Ex9_9_model
     description: 'Feedback Control of Dynamic Systems (Author: G. F. Franklin, J.
       D. Powell and A. Emami-Naeini), 9) Nonlinear Systems, 9.9) Describing Function
       for a saturation nonlinearity'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3432
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="5.0" title="Ex9_9_model"><!--Xcos - 1.0 - scilab-5.5.2
@@ -157624,14 +180606,52 @@
       as="geometry" height="40.0" width="40.0" x="360.0" y="140.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="-2dd55334:14dcbdd0183:-7fd3" parent="-2dd55334:14dcbdd0183:-7fd2"/></XcosDiagram>
     media: gallery136.png
+    script_dump: '//Example 9.9
+
+      //Describing Function for a saturation nonlinearity.
+
+
+      //Response of the saturation nonlinearity to sinusoidal input
+
+      //Describing Functin for saturation nonlinearity.
+
+      k=1;
+
+      N=1;
+
+      i=1;
+
+      Keq=[];
+
+
+      for a=0:0.2:10
+
+      if k*a/N > 1 then
+
+      Keq(i,1)=2/%pi*(k*asin(N/a/k)+N/a*sqrt(1-(N/k/a)^2))
+
+      else
+
+      Keq(i,1)=k
+
+      end
+
+      i=i+1;
+
+      end
+
+
+      a=0:0.2:10;
+
+      a=a'';'
 - model: saveAPI.gallery
-  pk: 759
+  pk: 138
   fields:
     save_id: gallery137
     name: Ex3_1
     description: 'Control Systems (Author: A Nagoor Kani), 3) TIME RESPONSE ANALYSIS,
       3.1) RESPONSE OF THE SYSTEM'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_1"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -158259,14 +181279,44 @@
       x="180.0" y="200.0"/></Array></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery137.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 3.1
+
+
+      s=%s
+
+      p=poly([4],''s'',''coeff'')
+
+      q=poly([0 5 1],''s'',''coeff'')
+
+      g=p./q
+
+      disp(g,''The given transfer function is'')
+
+      c=g/(1+g)
+
+      disp(c,''The closed loop transfer function is'')
+
+      u=c/s
+
+      disp(u,''The input is unit step signal'')'
 - model: saveAPI.gallery
-  pk: 760
+  pk: 139
   fields:
     save_id: gallery138
     name: Ex3_2
     description: 'Control Systems (Author: A Nagoor Kani), 3) TIME RESPONSE ANALYSIS,
       3.2) RESPONSE OF THE SYSTEM'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_2"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -158852,14 +181902,46 @@
       x="340.0" y="70.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery138.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 3.2
+
+
+      s=%s
+
+      p=poly([100],''s'',''coeff'')
+
+      q=poly([0 2 1],''s'',''coeff'')
+
+      h=poly([1 0.1 0 ],''s'',''coeff'')
+
+      g=p./q
+
+      disp(g,''the given transfer function is'')
+
+      c=g/(1+(g*h))
+
+      disp(c,''the closed loop transfer function is'')
+
+      u=c/s
+
+      disp(u,''the in put is unit step signal'')'
 - model: saveAPI.gallery
-  pk: 761
+  pk: 140
   fields:
     save_id: gallery139
     name: Ex3_6
     description: 'Control Systems (Author: A Nagoor Kani), 3) TIME RESPONSE ANALYSIS,
       3.6) RESPONSE OF THE SYSTEM'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_6"><!--Xcos - 1.0 - scilab-5.5.2 - 20181120--><mxGraphModel
@@ -159445,14 +182527,76 @@
       x="360.0" y="260.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery139.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 3.6
+
+
+      s=poly(0,''s'')
+
+      // the input is unit step signal
+
+      h=syslin(''c'',16/(s^2+4*s+16))//the value of k is 0.2
+
+      zeta=0.5//given damping ratio
+
+      disp(h,''the closed loop transfer function'')
+
+      //standard form od second order system is w^2/s^2+2*zeta*w*s+w^2
+
+      //compaing h with the standard form
+
+      w=4//natural frequency of oscillation
+
+      disp(w,''natural frequency of oscillation in rad/sec'')
+
+      k=(2*zeta*w-(0.8))/16
+
+      disp(k,''the value of k is'')
+
+      mp=exp((-zeta*%pi)/sqrt(1-(zeta)^2))*100//percentage peak overshoot
+
+      disp(mp,''percentage peak overshoot in percentage'')
+
+      tp=%pi/(w*sqrt(1-(zeta)^2))
+
+      disp(tp,''peak time in seconds'')
+
+      //constructing a right angle triangle with zeta and sqrt(1-zeta^2)
+
+      theta=atan(0.866/0.5)//(1-zeta^2)/zeta
+
+      disp(theta,''the value of theta is'')
+
+      tr=(%pi- theta)/(w*sqrt(1-(zeta)^2))
+
+      disp(tr,''the rise time in seconds'')
+
+      t=1/(zeta*w)//time constant
+
+      ts1=3*t//settling time for 5% error
+
+      disp(ts1,''settling time for 5% error in seconds'')
+
+      ts2=4*t//settling time for 2% error
+
+      disp(ts2,''settling time for 2% error in seconds'')'
 - model: saveAPI.gallery
-  pk: 762
+  pk: 141
   fields:
     save_id: gallery140
     name: Ex3_7
     description: 'Control Systems (Author: A Nagoor Kani), 3) TIME RESPONSE ANALYSIS,
       3.7) RESPONSE OF THE SYSTEM'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex3_7"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -160038,14 +183182,64 @@
       x="480.0" y="100.0"/><mxPoint as="targetPoint" x="480.0" y="170.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery140.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 3.7
+
+
+      s=%s
+
+      p=poly([1 0.4 0 ],''s'',''coeff'')
+
+      q=poly([0 0.6 1],''s'',''coeff'')
+
+      g=p./q
+
+      disp(g,''the given transfer function is'')
+
+      c=g/(1+g)
+
+      disp(c,''the closed loop transfer function is'')
+
+      u=c/s
+
+      disp(u,''the in put is unit step signal'')
+
+      //standard form od second order system is w^2/s^2+2*zeta*w*s+w^2
+
+      //compaing h with the standard form
+
+      w=1//natural frequency of oscillation
+
+      disp(w,''natural frequency of oscillation in rad/sec'')
+
+      zeta=1/(2*w)
+
+      disp(zeta,''the damping ratio is'')
+
+      mp=exp((-zeta*%pi)/sqrt(1-(zeta)^2))*100//percentage peak overshoot
+
+      disp(mp,''percentage peak overshoot in percentage'')
+
+      tp=%pi/(w*sqrt(1-(zeta)^2))
+
+      disp(tp,''peak time in seconds'')'
 - model: saveAPI.gallery
-  pk: 763
+  pk: 142
   fields:
     save_id: gallery141
     name: Ex7_10
     description: 'Control Systems (Author: A Nagoor Kani), 7) STATE SPACE ANALYSIS,
       7.10) STATE MODEL'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex7_10"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -160637,14 +183831,36 @@
       x="360.0" y="110.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery141.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 7.10
+
+
+      s=%s
+
+      p=poly([10],''s'',''coeff'')
+
+      q=poly([1 2 4 1],''s'',''coeff'')
+
+      sm=cont_frm(p,q)
+
+      disp(sm,''the state model in matrix form is'')'
 - model: saveAPI.gallery
-  pk: 764
+  pk: 143
   fields:
     save_id: gallery142
     name: Ex7_11
     description: 'Control Systems (Author: A Nagoor Kani), 7) STATE SPACE ANALYSIS,
       7.11) STATE MODEL'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex7_11"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -161236,14 +184452,36 @@
       x="270.0" y="210.0"/><mxPoint as="targetPoint" x="330.0" y="220.0"/></mxGeometry></ExplicitLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery142.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 7.11
+
+
+      s=%s
+
+      p=poly([40 10],''s'',''coeff'')
+
+      q=poly([0 3 4 1],''s'',''coeff'')
+
+      sm=cont_frm(p,q)
+
+      disp(sm,''the state model in matrix form is'')'
 - model: saveAPI.gallery
-  pk: 765
+  pk: 144
   fields:
     save_id: gallery143
     name: Ex7_12
     description: 'Control Systems (Author: A Nagoor Kani), 7) STATE SPACE ANALYSIS,
       7.12) STATE MODEL'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 3885
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="30.0" title="Ex7_12"><!--Xcos - 1.0 - scilab-5.5.2 - 20160406
@@ -161836,14 +185074,40 @@
       as="sourcePoint" x="360.0" y="120.0"/><mxPoint as="targetPoint" x="360.0" y="140.0"/></mxGeometry></CommandControlLink></root></mxGraphModel><mxCell
       as="defaultParent" id="0:2:0" parent="0:1:0"/></XcosDiagram>
     media: gallery143.png
+    script_dump: '//control systems by Nagoor Kani A
+
+      //Edition 3
+
+      //Year of publication 2015
+
+      //Scilab version 6.0.0
+
+      //operating systems windows 10
+
+      // Example 7.12
+
+
+      s=%s
+
+      h=syslin(''c'',(2*(s+5))/((s+2)*(s+3)*(s+4)))
+
+      disp(h,''thr transfer function is'')
+
+      ss=tf2ss(h)
+
+      disp(ss,''the state space model is'')
+
+      [Ac,Bc,U,ind]=canon(ss(2),ss(3))
+
+      disp(Ac,Bc,U,ind)'
 - model: saveAPI.gallery
-  pk: 766
+  pk: 145
   fields:
     save_id: gallery144
     name: example_11_1
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       11) Unsymmetrical Fault Analysis, 11.1) LG and 3Phase faults Comparision'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.25" title="example_11_1"><!--Xcos - 1.0 - scilab-5.5.2
@@ -162975,15 +186239,49 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitInputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="67e02cde:13157ae1f65:-8000" parent="67e02cde:13157ae1f65:-7fff"/></XcosDiagram>
     media: gallery144.png
+    script_dump: '//Chapter 11
+
+      //Example 11.1
+
+      //page 406
+
+      //To draw sequence networks of generator and to compare LG fault current will
+      be greater than three-phase fault current when neutral is solidly grounded
+
+
+      disp("Sequence networks of synchronous generator grounded through neutral impedance
+      has been drawn using XCOS ");
+
+
+      disp("Since the derivation can not be done here, let us do this problem by taking
+      a suitable values for the sequence reactances of the generator");
+
+
+      disp("X1=j0.18, X2=j0.15, X0=j0.10 pu and Ea=1");
+
+
+      disp("From the figs 11.13 and 11.14 in the textbook,we can find Ilg and I3L");
+
+
+      Ea=1;X1=0.18*%i;X2=0.15*%i;X0=0.10*%i;
+
+
+      IaLG=3*Ea/(2*X1+X0)
+
+      Ia3L=3*Ea/(3*X1)
+
+
+      disp("Same values of sequence impedance have been used in XCOS simulation also
+      to varify the result");'
 - model: saveAPI.gallery
-  pk: 767
+  pk: 146
   fields:
     save_id: gallery145
     name: example_11_2
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       11) Unsymmetrical Fault Analysis, 11.2) Grounding Resistor voltage and Fault
       Current'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.25" title="example_11_2"><!--Xcos - 1.0 - scilab-5.5.2
@@ -164135,15 +187433,53 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitInputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="67e02cde:13157ae1f65:-7afa" parent="67e02cde:13157ae1f65:-7af9"/></XcosDiagram>
     media: gallery145.png
+    script_dump: '//Chapter 11
+
+      //Example 11.2
+
+      //page 408
+
+      //To find fault current and voltage across the grounding resistor
+
+
+      X1eq=(%i*0.18)/2;
+
+      X2eq=(%i*0.15)/2;
+
+      Z0eq=(%i*0.10)+3*(2*20/(11^2));
+
+
+      Ea=1;
+
+
+      //calculation of fault current
+
+      printf(''\nFault current is given by '');
+
+      If=(3*Ea)/(X1eq+X2eq+Z0eq)
+
+
+      //current in grounding resistor
+
+      Ifg=abs(If)*(20/(11*sqrt(3)));
+
+      printf(''\n\nCurrent through grounding resistor Ifg=%0.2fkA'',Ifg);
+
+
+      //voltage across grounding resistor
+
+      Vgr=abs(If*(2*20/(11^2))*(11/sqrt(3)));
+
+      printf(''\n\nVoltage across grounding resistor Vgr=%0.2fkV\n\n'',Vgr);'
 - model: saveAPI.gallery
-  pk: 768
+  pk: 147
   fields:
     save_id: gallery146
     name: example_11_3
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       11) Unsymmetrical Fault Analysis, 11.3) Fault and subtransient currents of the
       system'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.25" title="example_11_3"><!--Xcos - 1.0 - scilab-5.5.2
@@ -165468,14 +188804,153 @@
       as="geometry" height="40.0" width="40.0" x="790.0" y="250.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="2af926ac:131590fb290:-7ef4" parent="2af926ac:131590fb290:-7ef3"/></XcosDiagram>
     media: gallery146.png
+    script_dump: '//Chapter 11
+
+      //Example 11.3
+
+      //page 409
+
+      //To find fault current and subtransient current in all parts of the system
+
+
+      a=-0.5+(sqrt(3)/2)*%i;
+
+
+      //neglecting prefault currents
+
+      Vf0=10/11;
+
+      Eg=Vf0; Em1=Vf0 ;Em2=Vf0;
+
+
+      //positive sequence network when it is replaced by its thevenin''s equvivalent
+      as shown in fig11.18
+
+      printf(''\nsequence impedances are given by \n'');
+
+      Z1=(%i*0.525*%i*0.23)/(%i*0.755);
+
+      Z2=Z1;
+
+      Z0=%i*1.712;
+
+      printf(''Z1=j%0.4f \nZ2=j%0.4f \nZ0=j%0.4f'',abs(imag(Z1)),abs(imag(Z2)),abs(imag(Z0)));
+
+      //to find sequence current
+
+      Ia1=Vf0/(Z1+Z2+Z0);
+
+      Ia2=Ia1;
+
+      Ia0=Ia1;
+
+
+      //to find fault current
+
+      If=3*Ia0;
+
+      printf(''\n\nFault Current= -j%0.4f'',abs(imag(If)));
+
+
+
+      //component current flowing from generator and motor
+
+      printf(''\n\nComponents currents flowing from Generator and motor are \n'')
+
+      Ig1=Ia1*(0.23/0.755) ;
+
+      Ig2=Ig1;
+
+      Ig0=0;
+
+      printf(''Ig1= -j%0.4f \nIg2= -j%0.4f \nIg0=%d'',abs(Ig1),abs(Ig2),abs(Ig0));
+
+      printf(''\n'');
+
+      Im1=Ia1*(0.525/0.755);
+
+      Im2=Im1;
+
+      Im0=Ia0;
+
+      printf(''\nIm1= -j%0.4f \nIm2= -j%0.4f \nIm0= -j%0.4f'',abs(Im1),abs(Im2),abs(Im0));
+
+
+      //fault currents from the generator and motor towards g are
+
+      printf(''\n\nFault current from the generator towards g are '');
+
+      Ig=[1 1 1;a^2 a 1;a a^2 1]*[Ig1;Ig2;Ig0];
+
+      disp(Ig);
+
+      printf(''and to g from motors are'');
+
+      Im=[1 1 1;a^2 a 1;a a^2 1]*[Im1;Im2;Im0];
+
+      disp(Im);
+
+
+      printf(''\nPositive sequence current =%0.3f pu'',(-%i*Ig1));
+
+      printf(''\nNegative sequence current =%0.3f pu'',(%i*Ig2));
+
+      printf(''\nZero sequence current=%d\n'',Ig0);
+
+
+      //under loaded condition,PU motor currents are
+
+      Im1o=(15/(25*0.909*0.8))*(0.800103636+%i*0.5998617938);
+
+      Im2o=(7.5/(25*0.909*0.8))*(0.800103636+%i*0.5998617938);
+
+      printf(''\nThe per unit motor currents are:\n'');
+
+      printf(''Motor1:%0.2f +j%0.3f pu'',real(Im1o),imag(Im1o));
+
+      printf(''\nMotor2:%0.2f +j%0.3f pu'',real(Im2o),imag(Im2o));
+
+
+      //the voltages behind subtransient reactances are calculated below
+
+      printf(''\n\nVoltage behind subtransient reactances:\n'');
+
+      printf(''Motor1:'');
+
+      Em1=Em1-(%i*0.345*Im1o);
+
+      printf(''Em1= %0.4f-j%0.4f'',real(Em1),abs(imag(Em1)));
+
+
+      printf(''\nMotor2:'');
+
+      Em2=Em2-(%i*0.69*Im2o);
+
+      printf(''Em2= %0.4f-j%0.4f'',real(Em2),abs(imag(Em2)));
+
+
+      printf(''\nGenerator:'');
+
+      Eg=Eg+(%i*0.525*(Im2o+Im1o));
+
+      printf(''Eg= %0.4fj+%0.4f'',real(Eg),abs(imag(Eg)));
+
+
+      //actual value of positive sequence current from generator and motor
+
+      printf(''\n\nThe actual value of positive sequence current from the generator
+      towards fault is = %0.2f+j%0.3f'',real(Im1o+Im2o+Ig1),imag(Im1o+Im2o+Ig1));
+
+      printf(''\nThe actual value of positive sequence current from the motors towards
+      fault is = %0.2f-j%0.3f'',real(-Im1o-Im2o+Im1),abs(imag(-Im1o-Im2o+Im1)));'
 - model: saveAPI.gallery
-  pk: 769
+  pk: 148
   fields:
     save_id: gallery147
     name: example_11_4
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       11) Unsymmetrical Fault Analysis, 11.4) LL Fault Current'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.25" title="example_11_4"><!--Xcos - 1.0 - scilab-5.5.2
@@ -166349,14 +189824,63 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="60.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-1f09110a:1315ad634dc:-8000" parent="-1f09110a:1315ad634dc:-7fff"/></XcosDiagram>
     media: gallery147.png
+    script_dump: '//Chapter 11
+
+      //Example 11.4
+
+      //page 412
+
+      //To find L-L fault current and voltage of healthy phase
+
+      X1eq=0.09*%i;
+
+      X2eq=0.075*%i;
+
+      Z0=0.99+(%i*0.1);
+
+      Ea=1;Ia0=0;
+
+
+      //to calculate Ia1
+
+      Ia1=Ea/(X1eq+X2eq);
+
+
+      //to calculate fault current
+
+      If=(-%i*sqrt(3))*(-%i*6.06);
+
+      Va1=Ea-(Ia1*X1eq);
+
+      Va0=(-Ia0*Z0);
+
+      Va2=Va1;
+
+
+      //voltage in healthy phase
+
+      Va=Va1+Va2+Va0;
+
+
+      //displaying the result
+
+      printf(''\nIa1=-j%0.2f'',abs(Ia1));
+
+      printf(''\nIf=%0.3f'',If);
+
+      printf(''\nVa1=Va2=%0.3f'',Va1);
+
+      printf(''\nVa0=%d'',Va0);
+
+      printf(''\nVa=Va1+Va2+Va0=%0.2f\n\n'',Va);'
 - model: saveAPI.gallery
-  pk: 770
+  pk: 149
   fields:
     save_id: gallery148
     name: example_11_5
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       11) Unsymmetrical Fault Analysis, 11.5) Double line to ground Fault'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.25" title="example_11_5"><!--Xcos - 1.0 - scilab-5.5.2
@@ -167388,14 +190912,75 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitInputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-1f09110a:1315ad634dc:-8000" parent="-1f09110a:1315ad634dc:-7fff"/></XcosDiagram>
     media: gallery148.png
+    script_dump: '//Chapter 11
+
+      //Example 11.5
+
+      //page 413
+
+      //To find Double line to ground fault current and voltage of healthy phase
+
+
+      Z1eq=0.09*%i;
+
+      Z2eq=0.075*%i;
+
+      Z0=(%i*0.1);
+
+      Ea=1;
+
+      a=(-0.5+%i*sqrt(3)/2);
+
+
+      //to find the sequence components of healthy phase
+
+      Ia1=Ea/(Z1eq+(Z2eq*Z0/(Z2eq+Z0)));
+
+      Va1=Ea-(Ia1*Z1eq);
+
+      Va2=Va1;
+
+      Va0=Va1;
+
+
+      Ia2=-(Va2/Z2eq);
+
+      Ia0=-(Va0/Z0);
+
+
+      I=[1 1 1;a^2 a 1;a a^2 1]*[Ia1; Ia2; Ia0];
+
+
+      //voltage of the healthy phase
+
+      Va=3*Va1;
+
+
+      //displaying the results
+
+      printf(''Ia1=-j%0.3f\n'',abs(Ia1));
+
+      printf('' Ia2=j%0.3f\n'',abs(Ia2));
+
+      printf('' Ia0=j%0.3f\n\n'',abs(Ia0));
+
+
+      printf('' Ia=%0.3f + j%0.3f\n'',real(I(1,1)),imag(I(1,1)));
+
+      printf('' Ib=%0.3f + j%0.3f\n'',real(I(2,1)),imag(I(2,1)));
+
+      printf('' Ic=%0.3f + j%0.3f\n\n'',real(I(3,1)),imag(I(3,1)));
+
+
+      printf('' Voltage of the healthy phase Va=3Va1=%0.3f'',Va);'
 - model: saveAPI.gallery
-  pk: 771
+  pk: 150
   fields:
     save_id: gallery149
     name: example_9_1_3phase_plot
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.1) Fault Current Calculation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: '<?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.2" title="example_9_1_3phase_plot"><!--Xcos - 1.0 -
@@ -170445,14 +194030,95 @@
       x="1590.0" y="550.0"/></TextBlock></root></mxGraphModel><mxCell as="defaultParent"
       id="-62268d13:130f6b46d8a:-7eeb" parent="-62268d13:130f6b46d8a:-7eea"/></XcosDiagram>'
     media: gallery149.png
+    script_dump: '//Chapter 9
+
+      //Example 9.1
+
+      //page 335
+
+      //To calculate fault current
+
+      //selecting base KVA and MVA
+
+      mvab=100;
+
+      Gmva=10;
+
+      T1mva=10; T2mva=5;
+
+      Gkvb=11; //generator kV base
+
+      OHLkvb=33; //overhead line kV base
+
+      Ckvb=6.6;// cable kB base
+
+      xg1=%i*0.15; xg2=%i*0.125; xt1=%i*0.10; xt2=%i*0.08;
+
+      xOHL=0.27+%i*0.36 ; xcab= 0.135+%i*0.08;
+
+
+      //clculating PU impedances
+
+
+      xg1=(xg1*mvab)/Gmva;
+
+      xg2=(xg2*mvab)/Gmva;
+
+      xt1=(xt1*mvab)/T1mva;
+
+      xt2=(xt2*mvab)/T2mva;
+
+      xOHL=(30*xOHL*mvab)/(OHLkvb^2);
+
+      xcab=(3*xcab*mvab)/(Ckvb^2);
+
+      //displaying results
+
+      printf(''\n Reactance of G1= j%0.1f pu \n'',abs(imag(xg1)));
+
+      printf('' Reactance of G2= j%0.1f pu\n'',abs(imag(xg2)));
+
+      printf('' Reactance of T1= j%0.1f pu\n'',abs(imag(xt1)));
+
+      printf('' Reactance of T2= j%0.1f pu\n'',abs(imag(xt2)));
+
+      printf('' Overhead line impedance=(%0.3f + j%0.3f) pu\n'',real(xOHL),abs(imag(xOHL)));
+
+      printf('' Cable impedance= (%0.3f + j%0.3f) pu\n'',real(xcab),abs(imag(xcab)));
+
+
+      // Impedance diagram is as shown in the figure9.7 in the textbook
+
+      // A XCOS simulation for this proble is done to explain the subtransient,transient
+      and steady state periods of a symmetrical short circuit
+
+      xtotal=((xg1*xg2)/(xg1+xg2)+xt1+xt2+xOHL+xcab);
+
+      Isc_pu=(1/xtotal);
+
+      Ibase=(mvab/(sqrt(3)*Ckvb))*1000;
+
+      Isc=Isc_pu*Ibase;
+
+      x_F_to_bus=(xt1+xt2+xOHL+xcab);
+
+      v_11b=x_F_to_bus*Isc_pu*11;
+
+      //displaying results
+
+      printf(''\nTotal impedance= %0.1f < %0.2f deg pu \n'',abs(xtotal),atand(imag(xtotal)/real(xtotal)));
+
+      printf(''Short circuit current= %d A\n'',abs(Isc));
+
+      printf(''Voltage at 11kV bus=%0.2f kV\n'',abs(v_11b));'
 - model: saveAPI.gallery
-  pk: 772
+  pk: 151
   fields:
     save_id: gallery150
     name: example_9_2
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.2) Subtransient and Momentary current Calculation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="example_9_2"><!--Xcos - 1.0 - scilab-5.5.2
@@ -171708,14 +195374,95 @@
       as="defaultParent" id="63eb11b3:131137cfac5:-8000" parent="63eb11b3:131137cfac5:-7fff"/><mxPoint
       as="origin" y="-20.0"/></XcosDiagram>
     media: gallery150.png
+    script_dump: '//Chapter 9
+
+      //Example 9.2
+
+      //page 337
+
+      //To calculate subtransient and momentary current
+
+      mvab=25;
+
+      Gmva=25;
+
+      T1mva=25; T2mva=25;
+
+      Gkvb=11; //generator kV base
+
+      OHLkvb=66; //overhead line kV base
+
+      Mkvb=6.6; //motor kV base
+
+      Mmva=5; //motor mva
+
+
+      XdG=%i*0.2; //Generator''s subtransient reactance
+
+      XdM=%i*0.25; //Motor''s subtransient reactance
+
+      XdM2=%i*0.3; //Motor''s transient reactance
+
+      Xt1=%i*0.1; // step up transformer''s reactance
+
+      Xt2=%i*0.1;//step down transformer''s reactance
+
+      Xtl=%i*0.15 ;//trnasmission line''s reactance
+
+
+      //per unit calculation
+
+      XdM=(XdM*mvab)/Mmva ;//perunit impedance of each motor
+
+      printf(''\nSubtransient reactance of each motor = j%0.2f pu\n'',abs(XdM));
+
+
+      //(a)subtransient current in the fault
+
+      Isc=(3*(1/XdM))+(1/(XdG+Xt1+Xt2+Xtl));
+
+      Ibase=(mvab*1000)/(sqrt(3)*Mkvb);
+
+      Isc=Isc*Ibase;
+
+      printf(''\nSubtransient current in the fault =%0.1fA\n'',abs(Isc));
+
+
+      //(b)subtransient current in the breaker B
+
+      IscB=(2*(1/XdM))+(1/(XdG+Xt1+Xt2+Xtl));
+
+      IscB=IscB*Ibase;
+
+      printf(''\nSubtransient current in breaker B=%0.1fA\n'',abs(IscB));
+
+
+      //(c) to find the momentary current through breaker B
+
+      ImomB=1.6*IscB;
+
+      printf(''\nMomentary current through the breaker B=%dA\n'',abs(ImomB));
+
+
+      //(d) to compute current to be interrupted by breaker in 5 cycles
+
+      XdM2=(XdM2*mvab)/Mmva ;//perunit transient impedance of each motor
+
+      IscB=(2*(1/XdM2))+(1/(XdG+Xt1+Xt2+Xtl));
+
+      IscB=IscB*Ibase;
+
+      ImomB=1.1*IscB;
+
+      printf(''\nCurrent to be interrupted by breaker B in five cycles=%dA\n'',abs(ImomB));'
 - model: saveAPI.gallery
-  pk: 773
+  pk: 152
   fields:
     save_id: gallery151
     name: example_9_3
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.3) Subtransient Current Calculation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="example_9_3"><!--Xcos - 1.0 - scilab-5.5.2
@@ -172773,14 +196520,79 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-487ef5e3:131246c8237:-8000" parent="-487ef5e3:131246c8237:-7fff"/></XcosDiagram>
     media: gallery151.png
+    script_dump: '//Chapter 9
+
+      //Example 9.3
+
+      //page 340
+
+      //To calculate subtransient current in Generator,Motor and fault
+
+      mvab=25;
+
+      kvb=11;
+
+      Vo=10.6/kvb; //PU Prefault voltage
+
+      printf(''\nPrefault Voltage = %0.4fpu\n'',Vo);
+
+
+      Load=15/mvab; //load PU with 0.8pf leading
+
+      Io=(Load/(Vo*0.8))*(cosd(36.9)+%i*sind(36.9)); //Prefault current
+
+      printf(''\nPrefault current = %0.4f at %0.1f deg  PU'',abs(Io),atand(imag(Io)/real(Io)));
+
+
+      Eg=Vo+(%i*0.45*Io); //voltage behind subtransient reactance(generator)
+
+      printf(''\n\nVoltage behind subtransient reactance(Generator) = %0.4f+j%0.2f
+      pu\n'''''',real(Eg),imag(Eg));
+
+
+      Em=Vo-(%i*0.15*Io); //voltage behind subtransient reactance(motor)
+
+      printf(''\nVoltage behind subtransient reactance(Motor) = %0.4f-j%0.4f pu'',real(Em),abs(imag(Em)));
+
+
+      Ig=Eg/(%i*0.45); //under fault condition
+
+      Im=Em/(%i*0.15); //under fault condition
+
+      printf(''\n\nUnder Faulted condition \n Ig""=%0.4f-j%0.4f pu'',real(Ig),abs(imag(Ig)));
+
+      printf(''\n Im""=%0.4f-j%0.4f pu'',real(Im),abs(imag(Im)));
+
+      If=Ig+Im; //Current in fault
+
+      printf(''\n\nCurrent in fault= -j%0.4f pu'',abs(imag(If)));
+
+
+      Ib=(mvab*1000/(sqrt(3)*11)); //Base current
+
+      //Actual Currents
+
+      printf("\n\nNow");
+
+      Ig=Ig*Ib
+
+      Im=Im*Ib
+
+      If=If*Ib
+
+      printf(''\nIg""= %0.1f-j%0.1f A'',real(Ig),abs(imag(Ig)));
+
+      printf(''\nIm""= %0.1f-j%0.1f A'',real(Im),abs(imag(Im)));
+
+      printf(''\nIf= -j%d A'',abs(imag(If)));'
 - model: saveAPI.gallery
-  pk: 774
+  pk: 153
   fields:
     save_id: gallery152
     name: example_9_4
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.4) Maximum MVA Calculation'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="example_9_4"><!--Xcos - 1.0 - scilab-5.5.2
@@ -173909,14 +197721,75 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="-8.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-487ef5e3:131246c8237:-7cc8" parent="-487ef5e3:131246c8237:-7cc7"/></XcosDiagram>
     media: gallery152.png
+    script_dump: '//Chapter 9
+
+      //Example 9.4
+
+      //page 345
+
+      //To calculate maximum MVA
+
+      mvab=50;
+
+      kvb=6.6;
+
+      mvaA=40;
+
+      mvaB=50;
+
+      mvaC=25;
+
+      feeder_impedance=((0.06+%i*0.12)*mvab)/(kvb^2)
+
+
+      Gen_A_reactance=(%i*0.1*mvab/mvaA);
+
+      Gen_B_reactance=(%i*0.1*mvab/mvaB);
+
+      Gen_C_reactance=(%i*0.1*mvab/mvaC);
+
+
+      printf(''\nGenerator A reactance = j%0.3f pu'',abs(Gen_A_reactance));
+
+      printf(''\nGenerator B reactance = j%0.3f pu'',abs(Gen_B_reactance));
+
+      printf(''\nGenerator C reactance = j%0.3f pu'',abs(Gen_C_reactance));
+
+
+      Reactor_A_reactance=(%i*0.12*mvab/mvaA);
+
+      Reactor_B_reactance=(%i*0.12*mvab/mvaB);
+
+      Reactor_C_reactance=(%i*0.12*mvab/mvaC);
+
+
+      printf(''\nReactor A reactance = j%0.3f pu'',abs(Reactor_A_reactance));
+
+      printf(''\nReactor B reactance = j%0.3f pu'',abs(Reactor_B_reactance));
+
+      printf(''\nReactor C reactance = j%0.3f pu'',abs(Reactor_C_reactance));
+
+
+      function resistance=parallel(r1,r2)
+
+      resistance=(r1*r2/(r1+r2));
+
+      endfunction
+
+
+      Z=(feeder_impedance)+parallel(%i*0.125,(%i*0.15 + parallel(%i*0.22,%i*0.44)));
+
+      scmva=(1/abs(Z))*mvab;
+
+      printf("\n\nSC MVA = %d MVA",scmva);'
 - model: saveAPI.gallery
-  pk: 775
+  pk: 154
   fields:
     save_id: gallery153
     name: example_9_5
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.5) Short Circuit Solution'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="0.5" title="example_9_5"><!--Xcos - 1.0 - scilab-5.5.2
@@ -175067,14 +198940,80 @@
       as="geometry" height="8.0" width="8.0" x="16.0" y="60.0"/></ImplicitOutputPort></root></mxGraphModel><mxCell
       as="defaultParent" id="-487ef5e3:131246c8237:-799b" parent="-487ef5e3:131246c8237:-799a"/></XcosDiagram>
     media: gallery153.png
+    script_dump: '//Chapter 9
+
+      //Example 9.5
+
+      //page 347
+
+      //To calculate short circuit solution
+
+      //referring to figures 9.19 in the text book,we get directly the fault current
+
+      V4o=1.0;
+
+      Zf=%i*0.13560;
+
+      If=V4o/Zf;
+
+      printf(''\nIf= -j%0.5f pu\n\n'',abs(If));
+
+
+      //From Fig9.19d
+
+      I1=If*((%i*0.19583)/(%i*0.37638));
+
+      I2=If*((%i*0.18055)/(%i*0.37638));
+
+      printf(''I1 = -j%0.5f pu \n\nI2 = -j%0.5f pu\n\n'',abs(I1),abs(I2));
+
+
+      //voltage changes for bus 1,2 and 3
+
+      deltaV1=0-(%i*0.15)*I1;
+
+      deltaV2=0-(%i*0.15)*I2;
+
+      printf(''DeltaV1=%0.5f pu\n\nDeltaV2=%0.5f pu\n\n'',deltaV1,deltaV2);
+
+
+      //reffering to book
+
+      V1f=1+deltaV1;
+
+      V2f=1+deltaV2;
+
+      printf(''V1f= %0.5f pu\n\nV2f=%0.5f pu\n\n'',V1f,V2f);
+
+      I13=(V1f-V2f)/(%i*0.15+%i*0.1);
+
+      printf(''I13=j%0.5f pu\n\n'',abs(I13));
+
+      deltaV3=0-((%i*0.15)*(I1)+(%i*0.15)*(I13));
+
+      Vf3=1+deltaV3;
+
+      printf(''DeltaV3=%0.5f pu\n\n'',deltaV3);
+
+      printf(''Vf3=%0.5f pu\n\n'',Vf3);
+
+      Vf4=0;
+
+      printf(''Vf4=%d\n\n'',Vf4);
+
+      //short circuit MVA at bus 4
+
+      SC_MVA_4=abs(If)*100;
+
+      printf(''Short circuit MVA at bus4 =%0.3f MVA'',SC_MVA_4);'
 - model: saveAPI.gallery
-  pk: 776
+  pk: 155
   fields:
     save_id: gallery154
     name: example_9_7
     description: 'Modern Power System Analysis (Author: D. P. Kothari And I. J. Nagrath),
       9) Symmetrical Fault Analysis, 9.7) Current Injection Method'
-    save_time: 2025-01-23 16:04:57+00:00
+    save_time: 2025-03-17 15:49:09+00:00
     book: 83
     data_dump: <?xml version="1.0" encoding="UTF-8"?><XcosDiagram background="-1"
       finalIntegrationTime="6.0" title="example_9_7"><!--Xcos - 1.0 - scilab-5.5.2
@@ -176287,3 +200226,37 @@
       as="geometry" height="40.0" width="40.0" x="600.0" y="350.0"/></TextBlock></root></mxGraphModel><mxCell
       as="defaultParent" id="75289c83:1315698632f:-8000" parent="75289c83:1315698632f:-7fff"/></XcosDiagram>
     media: gallery154.png
+    script_dump: '//Chapter 9
+
+      //Example 9.7
+
+      //page 355
+
+      //To evaluate Zbus using Current Injection method
+
+
+      disp("We can approach this problem using XCOS simulation")
+
+      disp("In this simulation");
+
+      disp("1)For injecting unit current at bus1 keeping bus2 open circuit,we use
+      a current source of 1 unit which is switched on from t=0 to t=2. During this
+      period we can observe the voltage waveforms of V1 and V2 and compare with the
+      results given in the textbook");
+
+      disp("2)For injecting unit current at bus2 keeping bus1 open circuit,we use
+      a current source of 1 unit which is switched on from t=4 to t=6. During this
+      period we can observe the voltage waveforms of V1 and V2 and compare with the
+      results given in the textbook");
+
+
+      Z11=7;
+
+      Z21=4;
+
+      Z12=Z21;
+
+      Z22=6;
+
+
+      Zbus=[Z11 Z12;Z21 Z22]'